School on Recent Advances in Strongly Correlated Quantum Materials

Correlated systems, where strong interactions among their constituents play a fundamental role, often exhibit remarkable phenomena. These systems display competing phases that can lead to novel ordered states and, potentially, to unexpected complex behavior. Despite the simplicity of defining their Hamiltonians, solving these systems is highly non-trivial, often requiring advanced analytical non-perturbative methods and numerical techniques.
Graduate courses often do not include many relevant developments in this field over the last 20 years. The primary goal of this school is to offer graduate students and postdocs a series of lectures that complement their foundational training.
The topics the school will cover are the following:
1. Recent advances in magnetism: frustrated magnets and altermagnets
2. Twisted bilayer materials
3. Numerical methods for strongly correlated systems

The Workshop “Novel Developments in Correlated Quantum Materials” will follow this School (October 12 – 16, at Principia Institute). 

Organizers:

• Victor L. Quito (USP, Brazil)
• José A. Hoyos (USP, Brazil)
• Thaís Victa Trevisan (USP, Brazil)

Announcement:

Application is now closed

Lecturers

• Thereza Paiva (UFRJ, Brazil): Numerical methods for strongly correlated systems
• Rodrigo Pereira (UFRN and IIP, Brazil): Recent advances in magnetism: frustrated magnets and altermagnets
• Alex Thomson (UC Davis, USA): Twisted bilayer materials

Announcement:

Application is now closed

TBC

Poster session 1 – October 5

• Alexander, Tony Maciel (USP, Brazil): Monte Carlo techniques applied to phase transitions in magnetic systems

This research project aims to study basic concepts of phase transitions and Monte Carlo techniques, applying them to the q-state clock model and the XY model on the square lattice with nearest and next-nearest frustrating neighbors. More specifically, the Ginzburg-Landau mean-field theory, the finite-size scaling theory, the Metropolis and heat bath local update algorithms, the Swendsen-Wang and Wolff non-local update algorithms, and, finally, the order-by-disorder mechanism have all been studied.

• Bellinati, Carlo (USP, Brazil): Evidence for the Dirac Spin Liquid in the Triangular Heisenberg Antiferromagnet

Representing fermionic Gaussian states (FGSs) as matrix product states (MPSs) provides a promising tool to connect parton theories and density matrix renormalization group (DMRG) simulations in the study of quantum spin liquids (QSLs). A notable example is the spin-$1/2$ $J_1$-$J_2$ antiferromagnetic Heisenberg model on the triangular lattice near $J_2/J_1 = 1/8$, for which parton studies suggest a gapless Dirac spin liquid (DSL) phase, while DMRG investigations have so far remained inconclusive. In this work, we propose a new algorithm for compressing FGSs into MPSs that combines the strengths of existing approaches while overcoming several of their limitations. Applying this method to the DSL ansatz on the triangular lattice, we show that key observations from recent DMRG studies, including the pair of quasi-degenerate ground states on cylindrical geometries and the excitation spectrum extracted from the MPS transfer matrix, are naturally explained within the parton framework, supporting the DSL as the ground state near the classical critical point.

• Boscolo, Mariana De Jesus (IFSC USP, Brazil): Fractal dispersion in one-dimensional models and its topological characterization: Hofstadter’s Butterfly in 1D.

This work presents a study of the generalized one-dimensional Aubry-André-Harper (AAH) model featuring a periodic modulation of the spin-orbit coupling parameter. The interplay between the length scales associated with the modulation and the lattice spacing gives rise to physics similar to that of electrons in a square lattice subjected to an external uniform transverse magnetic field. Here, we explore the similarities between these two models, demonstrating, for instance, the emergence of a fractal spectrum similar to the Hofstadter butterfly. The AAH model supports phases with non-trivial topology. We investigate the dependence of the fractal spectrum on the parameters of the model and provide a topological characterization of the energy gaps within the fractal spectrum.

• Costa, João Pedro Carvalho (University of Sao Paulo – Sao Carlos’s Institute of Physics, Brazil): Floquet engineering strongly correlated phases

Strongly correlated materials are characterized by the competition of multiple energy scales, often leading to exotic phases of matter, with unique fingerprints. Among them are frustrated magnets, which often present long-range entanglement and fractionalized excitations, and Kondo systems, which host exotic heavy-liquid phases and unconventional superconductivity. Several of these phases are difficult to obtain experimentally in equilibrium. Floquet engineering allows for an external way of driving and stabilizing phases in materials using periodic fields, such as monochromatic light. We consider the Floquet engineering of ruthenate and iridate Hubbard models, as well as a magic-angle twisted bilayer graphene (MATBG) heavy-fermion model. In frustrated magnets, we induce frustration by using circularly polarized light to enhance the Kitaev interaction and suppress the Heisenberg interaction, to melt the magnetic order observed in equilibrium conditions. In MATBG, we also use circular light to induce Kondo channels that did not exist in equilibrium, allowing competition between them to obtain an effective two-channel Kondo lattice.

• Duarte, João Chakrian Raphael Viana (Instituto de Física – Universidade Federal de Alagoas, Brazil): Phase Diagram and Quantum Critical Behavior of a Mixed-Spin Chain with Modulated Single-Ion Anisotropy

We investigate the quantum phases and critical properties of a mixed-spin (1, 1/2) antiferromagnetic Heisenberg chain with spatially modulated single-ion anisotropy. By employing Density Matrix Renormalization Group (DMRG) calculations, we construct the system’s ground-state phase diagram, revealing four distinct quantum states: a 1/3 magnetization plateau, a trivial non-magnetic (TnM) phase, a topological valence-bond-solid (TVBS) phase, and a gapless Luttinger liquid (LL) phase. These phases are characterized using local magnetization, transverse correlation functions, and entanglement-based diagnostics. While the TVBS phase is distinguished by localized edge modes and a doubly degenerate entanglement spectrum, the gapless LL phase is characterized by a power-law decay of spin correlations. We study the boundaries of the LL phase by extracting the Luttinger parameter, identifying two Kosterlitz-Thouless transition lines. Furthermore, the transition between the TVBS and TnM phases is identified as a topological quantum phase transition belonging to the Gaussian universality class. Using the tangential finite-size scaling method, we pinpoint the critical boundaries, verifying a conformal central charge of approximately 1.0 and obtaining continuously varying correlation length critical exponents. Our results highlight a rich phase diagram and show the interplay between spatial modulation, topological order, and quantum criticality in low-dimensional strongly correlated systems.

• Farinas, Pedro Sanchez (IFSC, USP, Brazil): Disorder in the Nematic Phase Transition of an Overdamped Model

We investigate the combined effects of quenched disorder and dissipation on the nematic phase transition described by a general C4 symmetric action coupling two order parameters. To elucidate the origin of disorder terms, we derive the effective theory starting from the random J1-J2 spin model. Random exchange interactions generate both random-mass and random-field contributions that couple directly to the nematic order parameter. In the regime J1<2J2, the low-energy nematic dynamics can be mapped onto an effective random transverse-field Ising model supplemented by random longitudinal fields. Dissipation is incorporated by coupling each effective Ising degree of freedom to an independent bath of harmonic oscillators. By extending the strong-disorder renormalization group (SDRG) to this problem, we demonstrate that the nematic phase is replaced by a novel inhomogeneous state composed of frozen nematic clusters without long-range order.

• Hernandez Cepeda, Nohora Alejandra (Ohio University, United States): Morphing polaron cloud near frustrated interfaces in Nagaoka ladders

The search for kinetic magnetism in strongly interacting systems has recaptured the attention of the quantum community, given the advances in the Hubbard model simulation in experimental platforms like cold atoms and moiré materials. As Nagaoka stated, a ferromagnetic ground state emerges in a square lattice when the system is doped away from half-filling, in the limit of infinite interactions. However, if a diagonal hopping (t′) is added to the square lattice, this ferromagnetic (FM) state becomes unstable as t′ takes over, giving rise to an antiferromagnetic (AFM) state. In this work, we investigate the presence of an interface where an abrupt change from non-frustrated to frustrated hoppings exists in a ladder geometry. By performing density matrix renormalization group (DRMG) simulations, we find that FM clouds (Nagaoka polarons) decay as t′ increases but without signs of spin-spiral behavior. At t′/t > 0.75 the system transitions to a striped phase where the polaron exhibits AFM order. Finally, we find that the nature of the magnetic correlations can be tracked by following the hole propagation in the ladder: a FM (AFM) polaron corresponds to a delocalized hole in the square (triangular) part of the ladder. This demonstrates that the hole propagation is essential for polaron formation, and that the presence of an interface delocalizes it asymmetrically, determining the magnetic character of the ground state polaron.

• Lima De Medeiros, João Roberto (IFMA, Brazil): Floquet Magnons in Placoid-like Magnetic Lattices

Spintronics emerged in the 1980s and, in less than five decades, has revolutionized the fundamental concepts of electronic circuits, which were traditionally governed by the presence and transport of charge. Its central premise is the expansion of the electronic paradigm by enabling information to be carried through an additional degree of freedom, the spin. One of the key perspectives in spintronics lies in the dynamics of spin waves, which offer advantages such as reduced energy dissipation, increased information capacity per carrier, enhanced non-volatility in memory devices, and improved optimization of the storage–processing relationship, thereby mitigating the von Neumann bottleneck. Numerous studies have explored these excitations in lattices with diverse topologies, aiming to exhaust their potential technological applications. These platforms provide a fertile ground for the development of fundamental components such as magnetic transistors, magnetic diodes, and logic gates, which are essential for modern computational architectures. Within this context, novel lattice geometries have attracted significant attention, including kagome and Lieb lattices. In particular, we highlight the placoid lattice, originally inspired by the geometry of fish scales found in predatory fish such as sharks and rays. This structure is known to enhance hydrodynamic performance and may offer analogous advantages for information transport in magnonic circuits. The present work aims to analyze a dynamic modulation of inter-site distances along the qy​ Direction, in the Brillouin Zone, following a periodic pattern. This induces an effective time-periodic Hamiltonian, creating favorable conditions for the emergence of exotic excitations known as Floquet magnons. These quasiparticles arise in out-of-equilibrium regimes, exhibiting nontrivial behaviors such as energy gap opening and the potential induction of topological phases. The study is based on the Heisenberg Hamiltonian, from which we derive the dispersion relation and evaluate key physical properties, including the energy spectrum,band structure, group velocity, presence of van Hove singularities, density of states, and density of states.

• Macedo De Mello, Diogo (Universidade de São Paulo, Brazil): An Overview of Dynamical Quantum Phase Transitions

Equilibrium phase transitions have been widely studied for nearly a century, resulting in a well-established theoretical framework. However, there is still a lack of understanding of the behavior of the non-equilibrium evolution of a strongly interacting quantum system. One phenomenon we can observe is a dynamical quantum phase transition (DQPT), a dynamical analogue of the equilibrium phase transition, in which a non-analytic behavior emerges at certain instants of time. The purpose of this work is to introduce the concept of DQPT, discussing its underlying physical mechanism, and build an intuition through a Bloch sphere visualization of the evolution.

• Nascimento, Artur Borges Coleta (UnB, Brazil): Entanglement, phase transitions, and dynamics in one-dimensional correlated models

The study of strongly correlated systems is central to modern condensed matter physics, as the interactions between particles give rise to emergent phenomena that defy independent-particle approximations. Understanding these behaviors is not only fundamental for characterizing complex materials – such as Mott insulators, unconventional superconductors, and novel magnetic phases – but also crucial for advancing quantum technologies, where artificial platforms like cold atoms in optical lattices and trapped ions allow for highly controllable realizations of model Hamiltonians. In these scenarios, the quantum entanglement resulting from strong correlations emerges as a fundamental resource for information processing and a powerful diagnostic tool. In this work, we review and systematize the behavior of non-local entanglement measures in closed correlated systems, focusing on spin chains and the Hubbard model. Utilizing exact diagonalization and density matrix renormalization group (DMRG) methods, we map out properties such as the von Neumann entropy, Rényi entropies, and the entanglement spectrum. In particular, we analyze how the initial entanglement structure of these states influences their non-equilibrium dynamics following global quantum quenches under unitary evolution. This work aims to establish a systematic understanding of how entanglement signatures characterize equilibrium phases and connect to the subsequent real-time quantum dynamics of many-body systems.

• Ramos, Lucas (Institute of Physics – Federal University of Mato Grosso do Sul, Brazil): Frustration effects on the magnetization plateau physics in a trimerized quantum spin-1/2 chain

We investigate frustration-induced instabilities in a trimerized quantum spin chain motivated by recent experimental findings for the compound Na$_2$Cu$_3$Ge$_4$O$_{12}$. Employing a cluster mean-field approach combined with Lanczos exact diagonalization, we analyze the ground-state and quantum-information properties of a Heisenberg model with competing interactions in a magnetic field. In the weakly frustrated regime, the system exhibits a robust $1/3$ magnetization plateau associated with a collective ferrimagnetic-like trimer state. Increasing the next-nearest-neighbor intratrimer coupling drives a pronounced reorganization of spin correlations, leading to a crossover toward a doublon-like correlation regime and providing a static ground-state picture consistent with the composite excitations observed dynamically in trimerized chains. The resulting low-energy behavior can be interpreted in terms of weakly interacting emergent spins, offering a microscopic explanation for the extended stability of the magnetization plateau. Furthermore, through finite-size scaling analyses of the energy gap, von Neumann entanglement entropy, and fidelity susceptibility, we characterize the zero-field criticality of the model. Ultimately, our results suggest that frustration gives rise to qualitatively distinct quantum states and provide a microscopic framework for understanding the emergence of fractionalized excitations in trimerized quantum spin systems. [1] arXiv:2606.13265

• Torrecilha, Elisa (Universidade de São Paulo, Brazil): A Tensor Renormalization Group Study of the Kagome J1-J2 Antiferromagnetic Ising Model in a field

The Kagome lattice antiferromagnetic Ising model is the prime example of a magnetically frustrated system. Here, it is not possible to satisfy all local energy constraints imposed by the magnetic Hamiltonian, leading to a highly degenerate ground state. Unlike many other planar models, such as the AF Ising model on the triangular lattice, the addition of a magnetic field or second-neighbor interactions does not fully quench the ground-state entropy, and order is achieved only through their combined effect. In this manner, there are many degenerate phases to study until the emergence of long-range order, each with its own particularities, such as emergent finite-T Kosterlitz-Thouless transitions or zero-temperature dimer maps. We have thoroughly studied these phases using a combination of the Tensor Renormalization Group – which allows us to directly access the free energy in the thermodynamic limit -, Monte Carlo simulations, and analytical arguments.

• Zúñiga, Julián Andrés (Instituto de Física La Plata, Argentina): Influence of the electric field on spintronic transport in trilayer pseudovalve heterostructures: interplay between exchange energy and spin–orbit coupling

Spintronics exploits the electron spin degree of freedom and magnetic order as fundamental variables for information storage and processing. In this context, magnetic tunnel junctions are essential devices, where tunnel magnetoresistance (TMR) enables the distinction between low- and high-resistance states associated with parallel and antiparallel magnetization configurations, making it a key mechanism in magnetic memory technologies. In this work, we present a theoretical study of spintronic transport in trilayer pseudovalve (PSV) heterostructures of the form Fe$_{90}$Cr$_{10}$/SC/Fe$_{90}$Cr$_{10}$, where the semiconductor (SC) acts as a tunnel barrier with a zinc-blende crystal structure. III–V semiconductors (GaSb, InSb, InAs, and GaAs) and the II–VI semiconductor ZnSe are considered, allowing a systematic analysis of the influence of different electronic properties and spin–orbit coupling (SOC) on quantum transport. The theoretical model is based on the Slonczewski formalism, incorporating the exchange energy in the Fe$_{90}$Cr$_{10}$ ferromagnetic electrodes, Dresselhaus and Rashba-type SOC in the semiconductor region, and the effect of an external electric field applied across the semiconductor barrier. The interplay among these mechanisms modifies the effective barrier potential and the wave-vector dynamics associated with the spin states during the tunneling process, thereby controlling the transmission probability and, consequently, the spin polarization and TMR. The TMR and spin polarization are calculated within the Landauer–Büttiker formalism as functions of the barrier thickness, crystallographic orientation, relative angle between the magnetization vectors, and the strength of the applied electric field. In the absence of an external electric field, the Fe$_{90}$Cr$_{10}$/GaSb/Fe$_{90}$Cr$_{10}$ heterostructure exhibits a maximum TMR of 83.60\%. Furthermore, the results show that the electric field significantly modulates spintronic transport by altering the relative contributions of spin–orbit coupling, with the Dresselhaus mechanism playing a more dominant role than the Rashba mechanism.

Poster session 2 – October 6

• Andrade, Pedro Lucas C. (Universidade Estadual do Maranhão, Brazil): Dzyaloshinskii–Moriya-Induced Topological Magnons in a Two-Dimensional Hybrid Breathing-Honeycomb Ferromagnet

Spin waves, or magnons, are collective excitations of ordered magnetic systems and provide a powerful route for investigating transport, stability, and topological phenomena in low-dimensional ferromagnets. In this work, we theoretically investigate magnon propagation in a two-dimensional Hybrid Breathing-Honeycomb ferromagnetic lattice, focusing on the emergence of nontrivial band structures induced by the Dzyaloshinskii–Moriya interaction. The system is described by a spin Hamiltonian containing Heisenberg exchange, Zeeman, anisotropic, and Dzyaloshinskii–Moriya terms. The latter is particularly relevant in the absence of inversion symmetry between magnetic sites and may open gaps at band-crossing points, giving rise to topological magnon bands. Using the spin-wave formalism and second quantization, the Hamiltonian is transformed into reciprocal space and written in terms of bosonic magnon operators. The resulting dynamical matrix allows the calculation of the magnon dispersion relation along high-symmetry directions of the Brillouin zone. Special attention is given to gap openings, band inversions, and signatures of nontrivial topology associated with Berry curvature and Chern numbers. The Hybrid Breathing-Honeycomb geometry introduces inequivalent magnetic bonds and competing exchange pathways, which may strongly affect the propagation of magnons and favor anisotropic spectral responses. Our results indicate that the interplay between lattice geometry and Dzyaloshinskii–Moriya interaction can generate topologically nontrivial magnonic features in two-dimensional ferromagnetic systems. These findings contribute to the theoretical understanding of engineered magnetic lattices and may be relevant for future applications in magnonics, spintronics, and low-dissipation information transport. [1] I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). [2] T. Moriya, Phys. Rev. 120, 91 (1960). [3] R. Matsumoto and S. Murakami, Phys. Rev. Lett. 106, 197202 (2011).

• Benlakhouy, Nadia (Mohammed VI Polytechnic University, Benguerir, Morocco, Morocco): Chiral limits and Floquet engineering of the Hofstadter butterfly in twisted bilayer graphene

Twisted bilayer graphene provides a unique platform to explore the interplay between moiré band structure, external fields, and emergent quantum phenomena. In this work, I investigate the Hofstadter butterfly spectrum in twisted bilayer graphene under a perpendicular magnetic field, focusing on the role of interlayer coupling and external driving. I show that the formation of the Hofstadter butterfly is primarily governed by AA-type interlayer hopping processes, in contrast to AB/BA hoppings that are responsible for flat-band physics. This leads to the identification of two distinct chiral limits in twisted bilayer graphene, each associated with different physical mechanisms. Furthermore, I analyze the impact of periodic driving using Floquet theory, considering both circularly polarized light and waveguide-induced fields. Circularly polarized light introduces an effective gap that breaks chiral symmetry and induces asymmetry in the energy spectrum, while waveguide light enables tunable control of interlayer couplings without breaking chiral symmetry. These results highlight the possibility of engineering electronic spectra and symmetries in moiré systems using external fields, providing insight into controllable regimes relevant to strongly correlated quantum materials.

• Calazans De Brito, Luis Filipe (University of São Paulo, Brazil): Evolution of localized pulses in the defocusing modified Korteweg–de Vries equation theory

In this work, we develop, in the Gurevich-Pitaevskii framework, an analytic theory for the evolution of localized pulses in the defocusing modified Korteweg–de Vries equation theory for situations when a dispersive shock does not eventually transform into a sequence of well-separated solitons. We found solutions to the Whitham modulation equations for the corresponding “quasisimple” dispersive shock waves and illustrated this solution with concrete examples of an initial pulse. Comparison of the analytical solution with direct numerical simulations showed that the modulation theory provides a very accurate description of the wave pattern even at one wavelength scale.

• De Assis Almeida, Patricia (Universidade de Sao Paulo, Brazil): Kondo Effect and thermoelectricity in strained Kagome materials

Understanding thermoelectric transport in materials with strong electronic correlations is crucial for designing high-efficiency devices. At low temperatures, the Kondo Effect drives the formation of the Kondo Resonance, a sharp peak in the electronic density of states near the Fermi energy level. This phenomenon is vital for optimizing the Seebeck coefficient, a key measure of thermoelectric conversion capacity. In this study, we apply the Single Impurity Anderson Model (SIAM), solved via the Numerical Renormalization Group (NRG) method, to analyze the transport properties in a novel system: an impurity coupled to a Kagome lattice nanoribbon. The Kagome lattice, known for its unique geometry and the presence of flat bands, provides an excellent platform to enhance electronic interactions and improve electrical conductivity. Furthermore, we introduce uniaxial strain as an external control tool to tune the electronic energy levels and, consequently, optimize the material’s thermoelectric performance. Our results demonstrate that the combination of the Kagome structure, the asymmetric positioning of the impurity level, and the application of uniaxial strain leads to remarkable improvements in the material’s Figure of Merit. The crucial ability to break electron-hole symmetry, essential for maximizing the Seebeck coefficient, is achieved by carefully tuning the impurity energy level. In summary, the precise simulations performed using the NRG provide clear guidelines for the rational design of highly efficient thermoelectric materials, specifically aiming at the maximization of the power factor. This work opens up significant possibilities for applications in energy harvesting and solid-state refrigeration systems. We acknowledge financial support of FAPESP, process 2025/21932-6.

• Duarte, Victor Gabriel Morele (Aeronautics Institute of Technology, Brazil): Dipoles near 2D materials: Where Dicke superradiance meets polaritonics

Surface exciton-polaritons strongly modify light-matter interactions at the nanoscale [1]. We show that dipole orientation is a marker of local excitation and collective radiative dynamics of emitters mediated by surface exciton-polariton modes. A set of modified transfer matrices for out-of-plane dipole moments based on Felderhof’s polarization sheet formalism [2] reveals a new polaritonic mode, enabling the reconstruction of emitter orientation through near-field optical microscopy [3]. Furthermore, using a Green-tensor framework, we find that this polaritonic mediation also reshapes the collective decay rate and far-field radiation of interacting emitters, producing orientation-dependent enhancement or suppression of Dicke superradiance. These results establish a direct link between exciton-polaritons and collective emission phenomena in structured two-dimensional photonic platforms. [1] Nature Mater 16, 182–194 (2017). [2] Appl. Phys. B 43, 161 (1987). [3] arXiv:2602.18149 (2026).

• Felix, Felipe Martins (Universidade Estadual de Campinas, Brazil): Electronic and magnetic properties of S-graphene compound

The experimental discovery of two-dimensional crystalline structures, such as graphene, has stimulated research due to their potential applications in several fields. The literature has reported stable carbon allotropes, such as S-graphene (SG), that exhibit Dirac cones. Additionally, a notable characteristic of S-graphene is the possibility of opening a gap at the Fermi level under lattice deformations. Motivated by these results, in this work we analyze the electronic and magnetic responses of the SG under structural deformations induced by strain using the Hubbard model. As a result, for the non-interacting case, this carbon allotrope can behave as (i) a band insulator, (ii) a Dirac semimetal, or (iii) a flat band insulator. We examine the interacting case using two different methodologies: mean-field theory and quantum Monte Carlo simulations, to determine the phase diagram of the model as a function of the strain and the electron-electron interaction. Interestingly, we notice the presence of semimetal, band insulator, and antiferromagnetic insulator states. Motivated by these results, we also perform first-principles calculations via Density Functional Theory (DFT), which indicate the presence of a spin-polarized phase as the lowest-energy state. The spatial distribution of the magnetization reveals that the central sites of the SG lattice are primarily responsible for the observed magnetic behavior. The theoretical predictions based on mean-field theory and DFT corroborate each other, demonstrating that applying strain to the SG structure plays a fundamental role in modulating its electronic and magnetic properties.

• Iroulart, Esteban Andrés (Instituto de Física de Líquidos y Sistemas Biológicos, Argentina): Skyrmion and meron phases induced by spin-phonon coupling

In chiral magnets, magnetic skyrmions are typically stabilized by the competition between ex change and Dzyaloshinskii-Moriya interactions under an external magnetic field, while the role of lattice degrees of freedom has received comparatively less attention. Here we study how spin-phonon (SP) coupling modifies magnetic interactions and the resulting spin textures in a two-dimensional skyrmion model in the square lattice. Using Monte Carlo simulations, we compare two simplified models describing the SP coupling: the Einstein site-phonon (ESP) and bond-phonon (BP) models. We find that ESP coupling stabilizes skyrmion crystals in field regimes that are topologically trivial in the uncoupled model and also induces additional textures, including meron-antimeron (M-aM) crystals and mixed skyrmion-bimeron (SkX-Bm) phases. Furthermore, for sufficiently strong phonon coupling, the conventional triple-q hexagonal skyrmion lattice is distorted into a double-q square skyrmion lattice. Overall, our results show that lattice effects provide a simple mechanism to tune topological magnetic phases.

• Loaiza Ospina, Sebastian (Universidad del Valle, Colombia): Characterization of non-trivial topology in a spin-1 Mott insulator

In recent years, so-called Kitaev materials have emerged as relevant platforms for the study of strongly correlated quantum phases, where spin–orbit coupling and anisotropic interactions give rise to phenomena such as quantum spin liquids, excitation fractionalization, and symmetry-protected topological phases. These phases exhibit robustness against external perturbations, making them of fundamental and technological interest within the broader context of quantum technologies. Most theoretical and experimental efforts have focused on spin-S=½ systems, where Majorana-like excitations and exotic topological phases may emerge. However, integer-spin systems, particularly S=1, display qualitatively distinct physics: beyond conventional dipolar order, additional multipolar degrees of freedom such as quadrupolar (nematic) order arise, together with topological phases such as the Haldane phase, which is characterized not by local symmetry breaking but by nonlocal order and protected edge modes. In this work, a spin-S=1 Mott insulator is studied as a quantum simulator implementable in optical lattice platforms, where the effective model is described by a bilinear–biquadratic Hamiltonian with Kitaev-type interactions [6]. The goal is to characterize topological phases both in equilibrium and under periodic driving (Floquet regimes), exploring the possibility of nontrivial topology “in time.” The characterization is carried out using numerical tools based on Lanczos exact diagonalization and analysis of the Floquet evolution operator.To characterize the physical abundance of these systems, tools such as (i) dynamical nonlocal correlations of the string-order type, (ii) the structure of the quasienergy spectrum, and (iii) entanglement measures as diagnostics of symmetry-protected phases. This approach establishes a connection between the physics of Kitaev materials, controllable quantum simulators, and the exploration of novel topological phases in interacting higher-spin systems, thus paving the foundations for the development of both new quantum technologies and fundamental physics.

• Marinho, Marcus (USP, Brazil): Inhomogeneous Vison Crystals

Geometric frustration in magnetic systems provides a fertile ground for the emergence of exotic states, ranging from quantum spin liquids to topological textures. In real materials, however, the unavoidable presence of disorder introduces a competing energy scale that can stabilize alternative states such as spin glasses or random singlets. In this context, the generalized antiferromagnetic Kitaev honeycomb model provides a remarkable platform to investigate the interplay between frustration and inhomogeneity. To perform this study, we formulate the model directly in real space, allowing for an exact treatment of disorder effects. In the clean limit, Lieb’s theorem ensures that the ground state of the pure Kitaev model resides in the zero flux sector. While weak magnetic fields open a gap that protects this phase, we find that third-neighbors interactions reduce the vison gap and promote flux proliferation, ultimately driving the system out of the zero flux configuration. Upon introducing bond disorder, we identify a critical disorder strength beyond which the formation of local visons becomes energetically favourable. The resulting vison distribution develops a remarkable negative tail, strongly suggesting that the true ground state is characterized by a spatially inhomogeneous gauge field.

• Pereira Castro, Lucas Taylor (Universidade Federal de Minas Gerais (UFMG), Brazil): Comparative Study of the Transition to Quantum Chaos in the Transverse Field Ising Model

We perform a comparative numerical analysis of the integrability-to-chaos transition in the Transverse Field Ising Model (TFIM). Our main focus is on investigating how different mechanisms of integrability breaking affect thermalization in the TFIM, as a framework with significant relevance to experimental dipolar magnets such as LiHo_xY_{1-x}F_4. In these materials, the application of a transverse field can induce random longitudinal components due to the mixing of crystal field states, fundamentally altering the system’s dynamics. We simulate the model’s evolution under two distinct perturbations: (i) the addition of a next-nearest-neighbor (NNN) interaction (J2), which preserves spin-parity (Z2) symmetry, and (ii) the addition of a longitudinal field (hz), which explicitly breaks this symmetry. Using Exact Diagonalization (ED) for chains up to $L=18$, we investigate the emergence of chaos through multiple static and dynamical diagnostics. The static diagnostics include level spacing statistics, the level spacing ratio (), the Eigenstate Thermalization Hypothesis (ETH) and entanglement entropy. The dynamical diagnostics are the growth of Lanczos coefficients as a proxy for Krylov complexity and the Spectral Form Factor (SFF). Our results confirm that both perturbations induce chaos in intermediate regimes. However, the analysis reveals fundamental differences. While the chaos induced by NNN interactions is robust, the longitudinal field triggers a re-entrance into an integrable-like regime at strong fields. This re-entrant behavior is marked by the loss of spectral rigidity, the emergence of level bunching in the energy spectrum, and a fragmented Hilbert space that hinders complete thermalization. We conclude that the mechanism of integrability breaking, particularly the preservation or violation of the Z2 symmetry, fundamentally dictates the robustness of quantum chaos and the efficiency of the thermalization process, providing insights into the thermalization of correlated quantum materials.

• Ribeiro, Matheus Franco (Universidade Federal do Paraná, Brazil): PT Symmetry Breaking and Extrinsic Altermagnetism in LaMnGe

LaMnGe (P4/nmm) belongs to the class of magneto-lamellar intermetallics, being a room temperature compensated antiferromagnet with 2D-like properties in the bulk due to the relatively large separation between the Mn planes in the crystal. As a system with combined parity and time reversal symmetry (PT), LaMnGe has spin-degenerate bands in accordance to Kramer’s theorem. However, the symmetry connecting the spin sublattices is not a simple translation, instead being a combined mirror operation in real space combined with a 180º rotation in spin space, compatible with altermagnetism. In this way, if the PT symmetry of the material is broken, an altermagnetic order may be activated via an external perturbation, thus being dubbed extrinsic altermagnetism. In comparison to intrinsic altermagnets, which are determined via the crystal symmetry exclusively, extrinsic altermagnets have the versatility of tuneable behavior and properties such as spin-splitting of the bands, opening new pathways for device architectures and fundamental physics. We study LaMnGe via density functional theory (DFT) subjected to different PT symmetry breaking conditions via external fields, concluding that the material is an extrinsic altermagnet with potential for magneto-optical devices as well as having a significant anomalous Hall effect signature.

• Tsypilnikov, Andrei (Instituto de Fisica, Universidade Federal Fluminense, Brazil): Floquet time crystal sensors: Fisher information and optimal observables for quantum enhanced metrology

Saturating the quantum Fisher information (QFI) bound with experimentally feasible measurements is a central challenge in quantum metrology. In this work, we address this problem within the method of moments (MoM), a practical estimation protocol. We first demonstrate that the symmetric logarithmic derivative (SLD) operator, when used as the observable in the MoM, exactly saturates the QFI bound. However, the SLD is generally a highly nonlocal and experimentally intractable operator. To bridge the gap between theoretical optimality and experimental feasibility, we consider a concrete sensing platform: a Floquet time crystal (FTC) acting as an AC field sensor. By analyzing the structure of the SLD for different relevant initial state preparations, we show that it can be faithfully approximated by simple, experimentally accessible observables—such as the bare spin magnetization or a parity operator. These approximations enable near-optimal quantum-enhanced sensing without requiring complex many-body measurements. Our results establish a systematic route to designing practical optimal observables for quantum sensors based on complex many-body systems and highlight the potential of Floquet time crystals for realistic quantum metrology applications.

Poster session 3 – October 8

• Barboza, Pedro Loureiro (Instituto de Física da Universidade de São Paulo, Brazil): Homogeneous and inhomogeneous strain in the XY model in the triangular lattice

In this work, we investigate the classical XY model on the triangular lattice with the symmetry-allowed 6-state clock anisotropy and strain. We first examine the role of this clock anisotropy in the model’s low-temperature behavior, with particular attention to the emerging critical phases. We then model uniaxial stress as a competing 2-state clock anisotropy. The competition between two-fold and six-fold anisotropies leads to a phase diagram with paramagnetic, two-fold-ordered, and four-fold-ordered phases, separated by Ising critical lines that indicate the destruction of the critical phase. We also investigate random strain, introduced through inhomogeneous spatial distortions of the triangular lattice, which could, for instance, originate from defects in the substrate. Together, competing anisotropies and structural disorder provide a controlled setting for assessing the Berezinskii-Kosterlitz-Thouless physics under realistic perturbations. Our results contribute to understanding how inhomogeneities and competing symmetry-breaking fields reshape phase transitions in frustrated two-dimensional systems.

• Bento Da Silva, Daniel (instituto de física da universidade de São Paulo, Brazil): Black solitons in spherical shell with LHY interation

a study of dark solitons on 2D spherical shells and its behave using simulations described by equations such as Gross-Pitaevski and the stability form

• Costa, Danielle Parente Da (Instituto de Física, Universidade de Brasília, Brazil): Equilíbrio e fora do equilíbrio do modelo de Hubbard estendido unidimensional

Sistemas fortemente correlacionados unidimensionais apresentam uma forte competição entre as energias cinéticas e potenciais e podem ser descritos pelo Modelo de Hubbard Estendido. Para uma cadeia de elétrons interagentes com interações locais e não-locais, seu hamiltoniano é dado pela energia no sítio (U), pela energia de interação entre sítios vizinhos (V) e pelo termo de hopping (t). O modelo tem um diagrama de fases rico contendo fases como ondas de densidade de spin (SDW), tripletos supercondutores (TS) e líquido de Luttinger (TLL). Embora tenha sido especialmente investigado no caso de interações puramente repulsivas, recentemente a investigação do quadrante correspondente a U > 0 e V < 0 (interação repulsiva coulombiana local e atrativa entre vizinhos) tem ganhado atenção, especialmente como modelo para cadeias de cupratos. Motivados por esse cenário, usamos neste trabalho o método DMRG na formulação MPS para investigar o Modelo de Hubbard Estendido nesse regime, tanto em equilíbrio quanto fora de equilíbrio. No regime de equilíbrio, observamos fases supercondutoras e regiões de separação de fase (PS1, PS2, PSx). Além disso, as correlações supercondutoras de singleto e tripleto apresentaram comportamento consistente com estudos anteriores. Para o regime fora do equilíbrio, partindo de um estado com partículas localizadas no centro da cadeia (PS2) em um quarto de preenchimento, realizamos quenches abruptos e lentos em V dentro do quarto quadrante, mantendo U fixo. Observamos a propagação das partículas ao longo da cadeia e, em todos os casos, o sistema relaxou para o perfil de ocupação do estado fundamental correspondente ao V final. A propagação das partículas é acompanhada por uma propagação espacial e temporal da entropia de emaranhamento e pela formação de correlações supercondutoras. Atualmente, o trabalho segue em andamento com a análise detalhada dos dados obtidos e a sistematização das diferentes respostas do sistema dependendo da “velocidade” do quench.

• De Figueiredo, Guilherme Fragoso (UNICAMP, Brazil): The $J_1$-$J_2$ antiferromagnet Heisenberg model with a Dzyaloshinskii-Moriya interaction in a honeycomb lattice: valence-bond solid phase and thermal Hall conductivity

We study the topological properties of a columnar valence-bond solid phase in a honeycomb lattice, in particular, we calculate the thermal Hall conductivity $\kappa_{xy}$ due to the elementary (triplon) excitations of this quantum paramagnetic phase. We consider a honeycomb lattice spin-$1/2$ $J_1$-$J_2$ antiferromagnetic Heisenberg model with an on-site anisotropy between the sites of the two triangular sublattices and in the presence of a Dzyaloshinskii-Moriya interaction between nearest-neighbor spins and an external magnetic field. Two (in-plane) Dzyaloshinskii-Moriya vector patterns are considered, both allowed by the symmetries of a honeycomb lattice with two distinct sites per unit cell. The columnar valence-bond solid phase is described within the bond-operator representation for the spin operators, a formalism that allows us to map the original Heisenberg model into an effective interacting boson model expressed in terms of triplet operators. We consider the effective boson model within the harmonic approximation and determine the region of stability of the valence-bond solid phase and triplon excitation bands. Moreover, the Berry curvatures and the Chern numbers of the triplon excitation bands are determined, as well as the temperature dependence of the thermal Hall conductivity due to triplons. Similar to a previous study concerning a square lattice columnar valence-bond solid [Phys. Rev. B 109, 134405 (2024)], we find that a Dzyaloshinskii-Moriya interaction indeed provides a finite Berry curvature for the triplon bands, but, in spite of that, the Chern numbers of the triplon bands vanish, yielding a phase characterized by topologically trivial elementary excitations; interestingly, the thermal Hall conductivity $\kappa_{xy}$ due to triplons is finite at low temperatures. Such a feature corroborates our previous findings concerning the square lattice columnar valence-bond solid that indicated that the no-go condition for a thermal Hall effect [Phys. Rev. Lett. 104, 066403 (2010)], previously determined for ordered magnets, might not be valid for a valence-bond solid phase.

• Farias Vasconcelos, Joao Lucas (Instituto de Física de São Carlos, Brazil): Intensifying superfluidity through atomic systems in mixed dimensions

This research aims to investigate the impact of long-range interactions on the quantum phase diagram of fermionic systems coupled to a three-dimensional bosonic bath. Building on a model designed to enhance p-wave superfluidity in two-dimensional fermionic layers, we analyze equilibrium states using advanced numerical techniques such as Quantum Monte Carlo simulations, which go beyond mean-field approximations. By exploring various confinement geometries—including infinite planes and bilayers—and considering dipole–dipole interactions mediated by phonon excitations from a Bose–Einstein condensate, we seek to identify exotic quantum phases and determine the critical conditions for superfluid transitions, paving the way for their future experimental observation.

• Fontenele, Rodrigo Alves (UFRJ, Brazil): Magnetism and Routes to Unconventional Superconductivity in an Effective Model for Magic-Angle Twisted Bilayer Graphene

Magic-angle twisted bilayer graphene (MATBG) has emerged as a remarkable platform for strongly correlated electron physics, displaying a rich interplay between symmetry-breaking phases, correlated insulating states, and unconventional superconductivity. Motivated by these developments, we investigate an effective topological heavy-fermion model proposed by Bernevig and collaborators as a low-energy description of MATBG. Using a self-consistent Hartree-Fock mean-field approach, we have explore the competition between different ordered states in the partially filled flat-band regime. In particular, we analyze valley-polarized (VP), intervalley coherent (IVC), and spin-polarized phases by comparing the internal energies associated with distinct mean-field ansätze. At half-filling of the active band, we find that the VP and IVC states are energetically degenerate and emerge alongside an effective ferromagnetic insulating phase. This state is characterized by the opening of a gap at the Fermi level and originates from a mixed valley-spin symmetry-breaking channel. In addition, on this characterization of the correlated ground state, we further discuss the role of doping in driving quantum critical behavior and possible routes toward unconventional superconductivity. Our results provide insight into the hierarchy of competing orders in MATBG-inspired effective models and establish a starting point for future studies incorporating fluctuations beyond the mean-field level.

• Khairnar, Gaurav Ramesh (Instituto de Física, Universidade de São Paulo, São Paulo, Brazil, India): Non-ergodic states in aperiodic quantum chains

The spin-1/2 XXZ chain under strong aperiodic modulation hosts a localized phase driven by emergent dimerization of renormalized couplings. Whether non-ergodicity persists across the full many-body spectrum remains an open question. Using exact diagonalization, we show that eigenstates throughout the spectrum are non-ergodic. We investigate routes to thermalization via a NNN J2 interaction and scaling of weak bonds. These results establish aperiodic-induced dimerization as a robust mechanism for non-ergodicity beyond the ground-state sector.

• Luna Ramos, Joseph André (UNICAMP, Brazil): Dynamics of Heisenberg chains with SU(N) using the Random Phase Approximation

Quantum Simulations have recently brought renewed interest to the Heisenberg Model with SU(N) symmetry. That is due the possibility for experimental realization reaching up to N=10. In this work, we use the Random Phase Approximation (RPA) to solve the equations of motion for atoms chains. As a result, we present the excitation’s spectrum and the Dynamical Structure Factor (DSF) for diferent values of N.

• Marino, Vito (SISSA, Italy): Influence of the inter-orbital interaction and kinetic terms on superconductivity: a simple two-orbital Hubbard model

A minimal two-orbital Hubbard model with nearest-neighbor hopping and no Hund’s coupling is investigated when the electron density is reduced from half filling.% ($n=2$). To focus on the electronic mechanisms of superconductivity, we restrict the variational ansatz to paramagnetic states and compute pairing correlations on top of optimized Jastrow-Slater wave functions. Here, superconducting correlations are highly enhanced by the presence of inter-orbital terms, such as on-site Coulomb repulsion $U’$ and nearest-neighbor hopping $\tilde{t}$. When considering $\tilde{t}=0$, a finite value of $U’$ effectively screens the intra-orbital repulsion $U$, producing a shift in the superconducting dome. Consequently, at moderately large values of $U$, inter-orbital repulsion yields a sizable increase in electron pairing compared to the single-orbital baseline. Furthermore, introducing a finite $\tilde{t}$ provides an additional boost to superconducting correlations, an effect driven by the simultaneous presence of flat and dispersive bands in the electronic structure.

• Queiroz Silveira, Lucas (Northeastern University, United States): Time and momentum resolved Floquet spectroscopy

Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, characterizing these transient regimes remains challenging, as conventional spectroscopic approaches often rely on equilibrium concepts that become inadequate. In this work, we introduce a time- and momentum-resolved tunneling spectroscopy protocol to probe the instantaneous energy structure of Floquet-driven systems beyond the high-frequency regime that does not depend on the prior knowledge of the entire spectrum.

• Soares, João Pedro (IFSC – USP, Brazil): Floquet Engineering Quadrupolar Chern Insulators
• Vela Wac, Atilio (Universidad Nacional de La Plata, Argentina): Competing quantum phases in a dipole-coupled model for one-dimensional polar metals

Polar metals have recently emerged as a fascinating class of quantum materials in which metallic conductivity coexists with broken inversion symmetry and polar distortions. Motivated by these systems, our research focuses on the numerical study of a one-dimensional strongly correlated model that combines electronic correlations, magnetism, and electric polarization. Using the Density Matrix Renormalization Group (DMRG), we investigate the ground-state properties of the system by analyzing magnetic, charge, and ferroelectric observables, with the aim of identifying the competing quantum phases and the mechanisms governing their stability. This work seeks to provide insight into the role of polar degrees of freedom in strongly correlated systems and to contribute to the understanding of emergent phenomena in low-dimensional polar metals

Venue: The event will be held at IFT-UNESP, located at R. Jornalista Aloysio Biondi, 120 – Barra Funda, São Paulo. The easiest way to reach us is by subway or bus, See arrival instructions here.

Accommodation: Participants whose accommodation will be provided by the institute will stay at Hotel Intercity the Universe Paulista. Hotel recommendations are available here.

Attention! Some participants in ICTP-SAIFR activities have received email from fake travel agencies asking for credit card information. All communication with participants will be made by ICTP-SAIFR staff using an e-mail “@ictp-saifr.org”. We will not send any mailings about accommodation that require a credit card number or any sort of deposit. Also, if you are staying at Hotel Intercity the Universe Paulista, please confirm with the Uber/Taxi driver that the hotel is located at Rua Pamplona 83 in Bela Vista (and not in Jardim Etelvina).

Attention! Some participants in ICTP-SAIFR activities have received email from fake travel agencies asking for credit card information. All communication with participants will be made by ICTP-SAIFR staff using an e-mail “@ictp-saifr.org”. We will not send any mailings about accommodation that require a credit card number or any sort of deposit. Also, if you are staying at Hotel Intercity the Universe Paulista, please confirm with the Uber/Taxi driver that the hotel is located at Rua Pamplona 83 in Bela Vista (and not in Jardim Etelvina).

BOARDING PASS: All participants, whose travel has been provided or will be reimbursed by ICTP-SAIFR, should bring the boarding pass  upon registration. The return boarding pass (PDF, if online check-in, scan or picture, if physical) should be sent to secretary@ictp-saifr.org by e-mail.

Visa information: Nationals from several countries in Latin America and Europe are exempt from tourist visa. Nationals from Australia, Canada and USA are required to apply for a tourist visa.

Accommodation: Participants, whose accommodation will be provided by the institute, will stay at Hotel Intercity the Universe Paulista. Hotel recommendations are available here.

Power outlets: The standard power outlet in Brazil is type N (two round pins + grounding pin). Some European devices are compatible with the Brazilian power outlets. US devices will require an adapter.

Poster presentation: Participants who are presenting a poster MUST BRING A PRINTED BANNER . The banner size should be at most 1 m (width) x 1,5 m (length). We do not accept A4 or A3 paper.

Badge: You will receive an identification badge upon registration, which must be used during the entire event. Without the badge, it may not be possible to enter the venue.

Security issues: Although São Paulo is a relatively safe city, be careful when using cellphones on the street, avoid isolated areas at night, and be aware when crossing the street that cars may not stop for pedestrians. Also, please do not leave valuable items like laptops unattended even for short breaks. At the IFT-UNESP, there are storage lockers available and keys can be obtained with our secretaries.