SCHOOL PROGRAM - Local: Anfiteatro Horácio Panepucci

Jan 23rd Jan 24th Jan 25th
8:45 - 9am
9 - 11am
1:30 - 3:30pm
4 - 6pm
Posters 1
Posters 2 & Closing


A historical overview of Tensor Networks

German Sierra (Consejo Superior de Investigaciones Cientificas)

Abstract: Tensor Networks are variational ansatzs to describe the low-energy states of quantum many-body systems in low spatial dimensions. Notable examples are Matrix Product States (MPS), Projected Entangled Pair States (PEPS), Multiscale Entanglement Renormalization Ansatz (MERA), etc. Tensor Networks were originally proposed in Condensed Matter Physics and Statistical Mechanics. Subsequently, Quantum Information Theory provided new knowledge and methods. More recently, the topic is merging with holographic ideas coming from string theory and high-energy physics. In this course we will present the main ideas and results following its historical development.

  • Class 1: The origins – Wilson Numerical Renormalization Group, Density Matrix Renormalization Group, Matrix Product States, Valence Bond States.
  • Class 2: Quantum Information Perspective – Projected Entangled Pair States, Multi-Scale Entangled Renormalization Ansatz.
  • Class 3: Infinite MPS and Conformal Field Theory – The XXZ model, The Haldane-Shastry model, The Kalmeyer-Laughlin wave function.

Equilibration properties of classical integrable field theories

Guiseppe Mussardo (International School for Advanced Studies – SISSA)

Abstract: We discuss the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper ℏ→0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the Generalized Gibbs Ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the Inverse Scattering Method.  

  • Class 1: Motivations and general background, Time evolution of classical fields, Local observables and their equilibration, Transfer matrix for thermal values of observables, Classical limit of quantum field theories.
  • Class 2:  Thermodynamics Bethe Ansatz, Form Factors.
  • Class 3: Inverse Scattering Method, Leclair-Mussardo formula.

Machine learning inspired variational methods: from matrix product states to neural networks

Adrian Feiguin (Northeastern University)

Lecture notes 1, 2, 3, and 4

Abstract: The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful numerical technique capable of treating dozens or hundreds of degrees of freedom with high accuracy, it is restricted to models that are not afflicted by the infamous sign problem. A powerful alternative is the use of variational techniques. In this series of lectures I will introduce variational approaches to study the quantum many-body problem in a new light, motivated by a convergence of ideas and concepts originated in machine learning. In particular, I will describe algorithms based on matrix product states and the use of neural networks as variational estimators for quantum states.

  • Class 1: Variational wave functions and their optimization.
  • Class 2: Matrix product states and DMRG.
  • Class 3: Applications: time-evolution and spectral functions.

Posters 1

William de Castilho and S. R. Salinas
Instituto de Física, Universidade de São Paulo

We analyze the thermodynamic behavior of a ferromagnetic mean-spherical model with three distinct spin components and the addition of Dzyaloshinkii-Moriya interactions. Exact calculations are performed for classical and quantum versions of this lattice model system. We show the onset of space modulated structures at low temperatures. 

William Carreras
Instituto de Física, Universidade de São Paulo


Guilherme Eduardo Freire Oliveira¹, Christian Maes², and Kasper Meerts²
¹Universidade Federal de Minas Gerais
²Katholieke Universiteit Leuven

We introduce a stochastic multi-photon dynamics on reciprocal space. Assuming isotropy, we derive the diffusion limit for a tagged photon to be a nonlinear Markov process on frequency. The nonlinearity stems from the stimulated emission. In the case of Compton scattering with thermal electrons, the limiting process describes the dynamical fluctuations around the Kompaneets equation. More generally, we construct a photon frequency diffusion process which enables to include nonequilibrium effects. Modifications of the Planck Law may thus be explored, where we focus on the low-frequency regime.

Gabriel Dias Carvalho1,2 and Pedro Silva Correia2
1Departamento de Física, Universidade Federal de Pernambuco
2Centro Brasileiro de Pesquisas Físicas

A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus given by the action of a coarse-graining channel, we have been able to recover information about the superposition coefficients of the system. We have also been able to visualize the death of quantum correlations between system and apparatus and the death of quantum coherences in the apparatus’ effective state, in the limit of a strong coarse-graining action—a situation akin to decoherence, although it is not necessary to evoke any interaction with the surrounding environment.

Pedro Henrique Mendes and Heitor C. M. Fernandes
Intituto de Física, Universidade Federal do Rio Grande do Sul

In this work we applied two unsupervised machine learning technics in the study of two models, Ising and Potts. Starting from final snapshots of the systems we could reduce the systems dimension and get insights in the
behaviour of the order parameters.

Gustavo O. Heymans1, N. F. Svaiter1, and G. Krein2
Centro Brasileiro de Pesquisas Físicas
Instituto de Física Teórica, Universidade do Estado de São Paulo

We investigate the low-temperature behavior of a system in a spontaneously broken symmetry phase described by a Euclidean quantum λΦ4d+1 model with quenched disorder. We study the effects of the disorder linearly coupled to the scalar field using a series representation for the averaged generating functional of connected correlation functions in terms of the moments of the partition function. To deal with the strongly correlated disorder in imaginary time, we employ the equivalence between the model defined in a d-dimensional space with imaginary time with the statistical field theory model defined on a space Rd⊗S1 with anisotropic quenched disorder. Next, using stochastic differential equations and fractional derivatives, we obtain the Fourier transform of the correlation functions of the disordered system at tree level. In one-loop approximation, we prove that there is a denumerable collection of moments of the partition function that can develop critical behavior. Our main result is that, even with the bulk in the ordered phase, there are many critical compactified lengths that take each of the moments of the partition function from an ordered to a disordered phase. This is a sign of generic scale invariance emergence in the system.

Danilo R. de Assis Elias, Enzo Granato, and Maurice de Koning
Intituto de Física Gleb Wataghin, Universidade Estadual de Campinas

We apply a set of machine-learning (ML) techniques for the global exploration of the phase diagrams of two frustrated 2D Ising models with competing interactions. Based on raw Monte Carlo spin configurations generated for random system parameters, we apply principal-component analysis (PCA) and auto-encoders to achieve dimensionality reduction, followed by clustering using the DBSCAN method and a support-vector machine classifier to construct the transition lines between the distinct phases in both models. The results are in very good agreement with available exact solutions, with the auto-encoders leading to quantitatively superior estimates, even for a data set containing only 1400 spin configurations. In addition, the results suggest the existence of a relationship between the structure of the optimized auto-encoder latent space and physical characteristics of both systems. This indicates that the employed approach can be useful in perceiving fundamental properties of physical systems in situations where a priori theoretical insight is unavailable.

Felipe D. Picoli and V. L. Líbero
Instituto de Física de São Carlos, Universidade de São Paulo

Cerium-based compounds exhibit important magnetic properties like a high magnetic anisotropy and diversity of magnetic orderings. These features result from the moderate localization of their f-state and its strong electronic correlation, in addition, to the crucial spin-orbit interaction [1]. In this direction, the Coqblin-Schrieffer formalism has been used to describe some of these magnetic properties since it incorporates the strong correlation and the spin-orbit interaction on the same foot to obtain an effective interaction energy between two neighbouring f-states [2]. This interaction has been successfully considered, with other sources of anisotropy, like christal-field
effects, to predict the magnetic behaviours of cerium monopnictides and monochalcogenides[1]. However, recent developments have observed and corrected some limitations and inconsistencies of this formalism, like the limitation for ions very far apart and the unphysical absence of the ionic
interchange symmetry [2]. With this new and corrected interaction energy, we have calculated the magnetic properties of some cerium compounds, mainly cerium monopnictides. We could predict the behaviour of the localized magnetic moments and their well-known phase transitions observed
experimentally, reducing the number of parameters required besides the ones already taken into account by the Coqblin-Schrieffer procedure.

[1] Bernard R. Cooper, Robert Siemann, David Yang, Pradeep Thayamballi and Aitava Banerjea, Handbook on the Physics and Chemistry of the Actinides, edited by A. J. Freeman and G. H. Lander, 1985.
[2] F. D. Picoli and V. L. Líbero, JMMM 550, 169062 (2022).

Lucas M. Ramos and F. C. Alcaraz
Instituto de Física de São Carlos, Universidade de São Paulo
Two new families of quantum spin chains with p multispin interactions were recently introduced in (1). One has Z(N) symmetry and describes free fermions (N=2) and parafermions (N>2) in the lattice (2). The other is an extension of XY model with N multispin interactions, having a large U(1) symmetry and is exactly solvable by Jordan-Wigner transformation. Both families are non-Hermitian for N>2 and under open boundary conditions they share quasi-energies obtained from the roots of a given characteristic polynomial. In this work, we show a general study of the conformal invariance properties and quantum information in a particular case of this new family of XY models. In this case, the quantum Hamiltonian has three spin interactions (p=2) and periodic boundary conditions. Although this model is non-Hermitian, the entanglement entropy (as von Neumann and Rényi entropy) is studied by exploring the translation invariance and using the correlation matrix technique.

(1) ALCARAZ, F. C.; PIMENTA, R. A. Free-parafermionic z(n) and free-fermionic xy quantum chains. Phys. Rev. E, American Physical Society, v. 104, p. 054121, Nov 2021.
(2) ALCARAZ, F. C.; PIMENTA, R. A. Free fermionic and parafermionic quantum spin chains with multispin interactions. Phys. Rev. B, American Physical Society, v. 102, p. 121101, Sep 2020.

Lair F. Trugilho and L. G. Rizzi
Departamento de Física, Universidade Federal de Viçosa

Temperature-dependent self-assembly processes in finite size volumes, i.e., spontaneous collective organization of a limited number of individual subunits, are present in a vast number of physical and biological systems, including those that involve macromolecular aggregation [1]. Aggregation phenomena have received particular interest due to the relation of protein aggregation with several human diseases, such as Alzheimer and type II diabetes [2]. Although the classical nucleation theory is the most popular approach that one might consider when describing aggregation, there is evidence of failure of that theory for systems where the particles present anisotropic interactions [3,4], as in the case of the amyloid protein aggregates related to the mentioned diseases. In this work, we consider the microcanonical characterization of a simple aggregation model, from which the equilibrium thermostatistics properties associated with the aggregation transition are obtained [5]. Besides, we apply the kinetic theory recently proposed in reference [6] to that model. This theory relates the equilibrium thermostatistics properties, such as latent heats and free-energy barriers, to the temperature-dependent rate constants. In particular, we performed stochastic simulations at different temperatures, from which the rate constants were numerically evaluated, and showed that the temperature-dependent rates estimated by our kinetic approach are in good agreement with the results obtained from the simulations [7]. We believe that our work may provide insights in the general problem of molecular aggregation. In addition, since the kinetic theory discussed here is model independent, it may be applied to more complex systems and provide experimentalists a useful method to access equilibrium thermostatistics properties of the aggregation transition from kinetic data.

[1] M. F. Hagan, G. M. Grason. Equilibrium mechanisms of self-limiting assembly. Rev. Mod. Phys. 93 025008 (2021).
[2] T. P. J. Knowles, M. Vendruscolo, C. M. Dobson. The amyloid state and its association with protein misfolding diseases. Nat. Rev. Mol. Cell Biol. 15 384-396 (2014).
[3] R. Cabriolu, D. Kashchiev, S. Auer. Breakdown of nucleation theory for crystals with strongly anisotropic interactions between molecules. J. Chem. Phys. 137 204903 (2012).
[4] R. J. Bingham, L. G. Rizzi, R. Cabriolu, S. Auer. Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules. J. Chem. Phys. 139 241101 (2013).
[5] L. F. Trugilho, L. G. Rizzi. Microcanonical characterization of first order phase transitions in a generalized model for aggregation. J. Stat. Phys. 186 40 (2022).
[6] L. G. Rizzi. Kinetics of first order phase transitions from microcanonical thermostatistics. J. Stat. Mech. 083204 (2020).
[7] L. F. Trugilho, L. G. Rizzi. Shape-free theory for the self-assembly kinetics in macromolecular systems. EPL. 137 57001 (2022).

Emanuel C. Diniz
Universidade do Estado de Mato Grosso

In this work, a sequel of Ref. [1], we investigate the dissipative dynamics of quantum resources such as entanglement, steering, and Bell non-locality in the Heisenberg one dimensional J1-J2 spin chain. We employ the microscopic master equation to probe such quantum resources, which give different results depending on the system configuration considering nearest neighbor and next nearest neighbor quantum resources. In particular, steering and Bell non-locality reaching considerable values within the microscopic model to small spin chain and tend to decrease as chain length increases.

[1] E. Diniz, A. Costa, and L. Castelano, Quantum resources of the steady-state of three coupled qubits: Microscopic versus phenomenological model, Physics Letters A 415, 127651 (2021).

Murilo Azambuja
Universidade Federal do Rio Grande do Sul

The Bardeen-Cooper-Schrieffer (BCS) theory is a paradigmatic example in the physics of many-body quantum mechanics. It is based on a model Hamiltonian in which an attractive interaction between electrons with energies near the Fermi energy is postulated, giving rise to a superconducting phase. Even though it succeeded in explaining the low critical temperature metallic superconductors, the theory for itself has some shortcomings. For example, it doesn’t elucidate the microscopic origins of the attractive electron-phonon interaction and also doesn’t include the Coulomb repulsion between electrons, not discussing its role in the formation of a superconducting phase. With the goal of obtaining more information about the microscopic origin of the electron-electron attractive interaction, we apply a Schrieffer-Wolff transformation in a interacting electron and phonon Hamiltonian, arising in an effective electron-electron interaction obtained from the electron-phonon interaction and show that with certain approximations we obtain the model Hamiltonian from the BCS theory. By including a Coulomb repulsion term between electrons in the
interacting electron-phonon Hamiltonian, we obtain the Anderson-Morel model, which shows that the electron-phonon interaction, by having the characteristics of a retarded interaction, plays an essential role in attenuating the effects of the repulsive Coulomb interaction and favors the formation of a superconducting phase.

Posters 2

Luiza Mayara Santos Miranda¹ and André Mauricio Conceição de Souza²
¹Centro Brasileiro de Pesquisas Físicas
²Departamento de Física, Universidade Federal de Sergipe

Presente em aproximadamente dois terços da população mundial, o vírus da herpes simplex gera problemas para humanidade desde a antiguidade. No entanto, não sabemos completamente tudo sobre o vírus, apesar dos diversos tratamentos e estudos, atualmente não há cura e a possibilidade da vacina é perspectiva futura. A infecção primária acontece quando o vírus entra contato com tecido epitelial e é permanente. Utilizando regras do modelo de autômatos celulares para estudar o comportamento do vírus no organismo, foram criadas simulações no Python modificando parâmetros importantes para infecção como o tempo que o sistema imunológico leva para reconhecer o vírus z, a probabilidade de nascer novas células no ambiente da infecção, as reinfeções e o comportamento sem a presença de células T de defesa. Os resultados obtidos a partir dessas variações de parâmetros estão de acordo o literatura, sem sistema imunológico o vírus no organismo se comporta de forma agressiva o que pode representar o início das infecções do vírus da herpes com os seres humanos, o sistema imune depende de z para reconhecer o vírus e a infecção é maior quando as células T demoram para reconhecer o vírus. Ao nascer células novas existe a possibilidade de serem infectadas novamente caso as suas células vizinhas
estejam infectadas, isso interfere nos resultados das simulações. Para reativação do vírus no hospedeiro quando o sistema imunológico enfraquece existe uma probabilidade de ocorrer infecções sintomáticas novamente porém o corpo leva menos tempo para reconhecer o vírus e elimina-los.

Angel Luis Leiva Stable
Instituto de Física, Universidade de São Paulo

Brownian particles interacting sequentially with distinct temperatures
and driving forces at each stroke have been tackled as a reliable
alternative for the construction of engine setups. However they can
behave very inefficiently depending on the driving used for the
worksource and/or when temperatures of each stage are very different
from each other. Inspired by some models for molecular motors and recent
experimental studies, a coupling between driving and velocities is
introduced as an alternative ingredient for enhancing the system
performance. Here, the role of this new ingredient for levering the
engine performance is detailed investigated from stochastic thermodynamics. Exact expressions for quantities and distinct
maximization routes have been obtained and investigated. The search of
an optimal coupling provides a substantial increase of engine
performance (mainly efficiency), even for large ΔT. A simple and general
argument for the optimal coupling can be estimated, irrespective the
driving and other model details.

Carlos E. Fernández Noa
Instituto de Física, Universidade de São Paulo

The construction of efficient thermal engines operating at finite times constitutes a fundamental and timely topic in nonequilibrium thermodynamics. We introduce a strategy for optimizing the performance of Brownian engines, based on a collisional approach for unequal interaction times between the system and thermal reservoirs. General (and exact) expressions for thermodynamic properties and their optimized values are obtained, irrespective of the driving forces, asymmetry, temperatures of reservoirs, and protocol to be maximized. Distinct routes for the engine optimization, including maximizations of output power and efficiency with respect to the asymmetry, the force, and both of these, are investigated. For the isothermal work-to-work converter and/or a small difference in temperature between reservoirs, they are solely expressed in terms of Onsager coefficients. Although the symmetric engine can operate very inefficiently depending on the control parameters, the usage of distinct contact times between the system and each reservoir not only can enhance the machine performance (signed by an optimal tuning ensuring the largest gain) but also enlarges substantially the machine regime operation. The present approach can pave the way for the construction of efficient Brownian engines operating at finite times.

Murilo Garcia
Universidade Estadual Paulista “Júlio de Mesquita Filho”


Mateus Guimarães
Intituto de Fisica, Universidade Federal do Rio Grande do Sul

The current work use neural networks (ResNets) to obtain the temperature of systems based on the spins configurations in the square lattice for the Potts Model with q-states such that q ∈ {2, 3, 4, 6, 7, 8}. We based the use of neural networks to solve the problem using the Statistical Learning framework due to the great generalization ability of deep neural networks; the steps and parameters for training a network under the perspective of the Supervised Learning are also presented and discussed. From the uncertainty associated with the proposed regression technique by neural network, one can find the transition temperatures for all studied q-states, which means that all exact transition temperatures are contained within the range of temperatures found by the applied method. Finally, we sought to illustrate differences in the uncertainty curves which could characterize the different orders of phase transitions in the Potts Model, however, it was not possible to separate the two types transition with current results; in an attempt to unravel the functioning of the residual neural network, we studied the feature maps of the convolutional layers, however it was not possible to base their performance on the perspective of physics. There is also some comments on the Monte Carlo Method used in the simulations of the Potts Model and comments on the Swendsen-Wang and Metropolis algorithms a complete description for the reproduction of the results is presented as well.

Guilherme Silva
Instituto de Ciências Matemáticas e Computação, Universidade de São Paulo
It has been known since the 1990s that fluctuations of eigenvalues of random matrices, when appropriately scaled and in the sense of one-point distribution, converge to the Airy2 point process in the large matrix limit. In turn, the latter can be described by the celebrated Tracy-Widom distribution. In this talk we discuss recent findings of Ghosal (MIT) and myself, showing that certain statistics of eigenvalues also converge universality to appropriate statistics of the Airy2 point process, interpolating between a hard and soft edge of eigenvalues. Such found statistics connect also to the integro-differential Painlevé II equation, in analogy with the celebrated Tracy-Widom connection between Painlevé II and the Airy2 process.

Patrícia A. Almeida, L. S. Sousa, T. M. Schmidt, G. B. Martins
Instituto de Física, Universidade Federal de Uberlândia

We study the properties of flat bands that appear in a heterostructure composed of strands of different widths of graphene armchair nanoribbons. One of the flat bands is reminiscent of the one that appears in pristine armchair nanoribbons and has its origin in a quantum mechanical destructive interference effect, dubbed “Wannier orbital states” by Lin et al. (Phys. Rev. B 79, 035405 (2009)). The additional flat bands found in these heterostructures, some reasonably closer to the Fermi level, seem to be generated by a similar interference process. After doing a thorough tight-binding analysis of the band structures of the different kinds of heterostructures, focusing in the properties of the flat bands, we use Density Functional Theory to study the possibility of magnetic ground states when placing, through doping, the Fermi energy close to the different flat bands. Our DFT results confirmed the expectation that these heterostructures, after being appropriately hole-doped, develop a ferromagnetic ground state that seems to require, as in the case of pristine armchair nanoribbons, the presence of a dispersive band crossing the flat-band. In addition, we found a remarkable agreement between the tight-binding and DFT results for the charge density distribution of the so-called Wannier orbital states.

Lucas S. Ferreira
Instituto de Física de São Carlos, Universidade de São Paulo

The phase transition in the 1D Ising model only happens at T=0, but through analysis of the model using the transfer matrix technique taking in count the two autovalues to compute the free energy and yours derivatives (second and fourth) we show a finite size scaling effect. In this finite-size scaling anomaly, the temperature in which the system changes your order is dependent on the size of the system. An approximation for this temperature is given and the number of the atoms used in the experimental results is estimated. We conclude that the finite system shows effects analogous to the infinity one and that the size of the lattice used in the experiment is large, but less than necessary to reach the limit T=0, needing infinity atoms.

Artur Domingues
Instituto de Física de São Carlos, Universidade de São Paulo


Ana Luiza N. Dias and Ronald Dickman
Universidade Federal de Minas Gerais

Active matter is a group of individuals that continuously consume energy to move in the enviroment. They are found in nature at different scales, for example flocks of birds and colonies of bacteria, and outside the biological field, systems such as a collection of vibrating motors. Despite the clear differences between these systems, they have in common the emergence of collective motion. Understanding how collective motion arises is the main goal of the study of active matter. The Vicsek model was the first to obtain results consistent with observations of groups of self-propelled organisms, showing that the emergence of collective behavior can be treated as a phase transition dependent on density and noise, and whose order parameter is associated with the velocity of particles. From it, new models with different features were created showing a rich variety of behaviors that can arise in the dynamics of interacting self-propelled individuals. In this work I study the behavior of an active matter model on a triangular lattice subject to an alignment interaction, and to excluded volume, using a mean-field approximation. Analyzing the evolution of the probabilities for the occupation of sites in the lattice, we find that the model goes through a discontinuous phase transition in which a particular direction of motion dominates.

Pedro A da Silva¹, Ricardo Jr. C. Lopes², and Afrânio R. Pereira¹
¹Universidade Federal de Viçosa

In this work we study a generalization of the XY model in two dimensions proposed by Romano and Zagrebnov[ for high values of generalized parameter by using monte carlo method. The nature of the phase transition is discussed based on the results of energy, specific heat and vortice density, in agreement with theoretical results of Shlosman, a change in the nature of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition to a first-order phase transition is observed.

Sasa Salmen¹ and Tereza C. Mendes²
¹Curso de Ciências Moleculares, Universidade de São Paulo
²Intituto de Física de São Carlos, Universidade de São Paulo

We aim to analyze the efficiency of three different algorithms (Heat Bath, Metropolis and Worm Algorithms) for the numerical simulation of the 2d Ising model. In particular, we plan to discuss the differences in efficiency considering GPU computations when compared to tradicional CPU runs. As a way to speed up our analysis, including a broader range of tested parameters in our optimization study, we may employ artificial intelligence models.