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Brazilian Journal of Physics

Special issue: Brazilian School on Statistical Mechanics, 2002 (Escola Brasileira de Mecânica Estatística, EBME)

Francisco Castilho Alcaraz, Silvio R. A. Salinas

Published Mar 1, 2003• 5 citations
Publisher

Abstract

Mecânica Estatística, EBME)The 2002 version of the Brazilian School on Statistical Mechanics (Escola Brasileira de Mecânica Estatística, EBME), which is hoped to happen every two years, took place from February 18 to March 1st, at the Instituto de Física de São Carlos, University of São Paulo, in the relatively small town of São Carlos, about 250 km from São Paulo.It was conceived as an answer to the need of a thematic school in statistical mechanics, at a national level, in order to promote short graduate courses on a variety of subjects and research topics that are relatively recent and not so well represented in the country.The school consisted of four short courses of approximately 10 hours, attended by about 70 students from several regions of Brazil, and whose lecture notes are finally being published in this special issue of the Braz.J. Phys.In the first week of the school, there were two courses: "Introduction to Bosonization" by Eduardo Miranda, from the University of Campinas, and "Introduction to Quantum Monte Carlo Simulations for Fermionic Systems", by Raimundo R. dos Santos, from the Federal University of Rio de Janeiro.In the second week, there were two other courses: "An Introduction to Numerical Methods in Low-Dimensional Quantum Systems", by André L. Malvezzi, from the Universidade Estadual Paulista, in Bauru, São Paulo, and "Non-Equilibrium Phase Transitions", by Ronald Dickman, from the Federal University of Minas Gerais, in Belo Horizonte.The highly pedagogical notes of Eduardo Miranda, which are selfcontained and assume just some basic knowledge of second quantization, are of particular relevance as an introduction to the use of the modern bosonization techniques.Raimundo Santos presented a tutorial introduction to Monte Carlo techniques for simulations of classical and quantum systems, with particular emphasis on the determinantal quantum Monte Carlo method.This short course was designed to provide the necessary tools for carrying out a numerical analysis of fermionic systems such as the well-known Hubbard model.André Malvezzi presented a comprehensive and systematic overview, including details of implementation, of the Lanczos and the Density Matrix Renormalization methods, which are by far the most common numerical techniques to obtain the eigenspectra of quantum chains.In the last short course, Ronald Dickman presented some applications of several techniques (mean-field, series expansions, renormalization-group) to the analysis of non-equilibrium phase transitions in stochastic systems.Since most of these topics had already been covered in a recent book, Dickman decided to send us a paper on path integrals and perturbation theory for stochastic processes, with a number of applications for nonequilibrium systems.

DOI
10.1590/s0103-97332003000100001

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Mecânica Estatística, EBME)The 2002 version of the Brazilian School on Statistical Mechanics (Escola Brasileira de Mecânica Estatística, EBME), which is hoped to happen every two years, took place from February 18 to March 1st, at the Instituto de Física de São Carlos, University of São Paulo, in the relatively small town of São Carlos, about 250 km from São Paulo.It was conceived as an answer to the need of a thematic school in statistical mechanics, at a national level, in order to promote short graduate courses on a variety of subjects and research topics that are relatively recent and not so well represented in the country.The school consisted of four short courses of approximately 10 hours, attended by about 70 students from several regions of Brazil, and whose lecture notes are finally being published in this special issue of the Braz.J. Phys.In the first week of the school, there were two courses: "Introduction to Bosonization" by Eduardo Miranda, from the University of Campinas, and "Introduction to Quantum Monte Carlo Simulations for Fermionic Systems", by Raimundo R. dos Santos, from the Federal University of Rio de Janeiro.In the second week, there were two other courses: "An Introduction to Numerical Methods in Low-Dimensional Quantum Systems", by André L. Malvezzi, from the Universidade Estadual Paulista, in Bauru, São Paulo, and "Non-Equilibrium Phase Transitions", by Ronald Dickman, from the Federal University of Minas Gerais, in Belo Horizonte.The highly pedagogical notes of Eduardo Miranda, which are selfcontained and assume just some basic knowledge of second quantization, are of particular relevance as an introduction to the use of the modern bosonization techniques.Raimundo Santos presented a tutorial introduction to Monte Carlo techniques for simulations of classical and quantum systems, with particular emphasis on the determinantal quantum Monte Carlo method.This short course was designed to provide the necessary tools for carrying out a numerical analysis of fermionic systems such as the well-known Hubbard model.André Malvezzi presented a comprehensive and systematic overview, including details of implementation, of the Lanczos and the Density Matrix Renormalization methods, which are by far the most common numerical techniques to obtain the eigenspectra of quantum chains.In the last short course, Ronald Dickman presented some applications of several techniques (mean-field, series expansions, renormalization-group) to the analysis of non-equilibrium phase transitions in stochastic systems.Since most of these topics had already been covered in a recent book, Dickman decided to send us a paper on path integrals and perturbation theory for stochastic processes, with a number of applications for nonequilibrium systems.
This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School ``Integrability in Atomic and Condensed Matter Physics'' in the summer of 2018. The responsibility for the selection of the material is partially with the organisers, Jean-Sebastien Caux, Nikolai Kitanine, Andreas Klümper and Robert Konik. The school had its focus on the application of integrability based methods to problems in non-equilibrium statistical mechanics. My lectures were meant to complement this subject with background material on the equilibrium statistical mechanics of quantum spin chains from a vertex model perspective. I was asked to provide a minimal introduction to quantum spin systems including notions like the reduced density matrix and correlation functions of local observables. I was further asked to explain the graphical language of vertex models and to introduce the concepts of the Trotter decomposition and the quantum transfer matrix. This was basically the contents of the first four lectures presented at the school. In the remaining two lectures I started filling these notions with life by deriving an integral representation of the free energy per lattice site for the Heisenberg-Ising chain (alias XXZ model) using techniques based on non-linear integral equations. Up to small corrections the following sections 1-6 display the six lectures almost literally. The only major change is that the example of the XXZ chain has been moved from section 5 to 2. During the school it was not really necessary to introduce the model, since other speakers had explained it before. But for these notes I thought it might be useful to introduce the main example rather early. I also supplemented each lecture with a comment section which contains additional references and material of the type that was discussed informally with the participants.
This manuscript is the collection of lectures given in the summer school on strongly correlated electron systems held at Isfahan university of technology, June 2007. A short overview on quantum magnetism and spin systems is presented. The numerical exact diagonalization (Lanczos) alghorithm is explained in a pedagogical ground. This is a method to get some ground state properties on finite cluster of lattice models. Two extensions of Lanczos method to get the excited states and also finite temperature properties of quantum models are also explained. The basic notions of quantum phase transition is discussed in term of Ising model in transverse field. Its phase diagram and critical properties are explained using the quantum renormalization group approach. Most of the topics are in tutorial level with hints to recent research activities.
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Quantum field theory can be seen as a set of methods and ideas that, besides its importance in the study of the elementary particles, has been widely used in other areas.In particular, it constitutes an indispensable framework in the modern approach to phase transitions and critical phenomena.The origin of this constant relationship between field theory and condensed matter is due to the fact that despite their superficial differences, both deal with problems involving a large number of degrees of freedom.Thus, it is not surprising that the same techniques may be useful in both fields.This work addresses problems in these two areas and it is essentially divided in two parts.The first part is devoted to the study of field theories with an anisotropy between space and time, which implies a breaking of the Lorentz symmetry.One of the motivations for considering this kind of theory is precisely the study of phase transitions in condensed matter systems.Renormalization group analysis with emphasis on the possibility of restoration of the Lorentz symmetry and also a discussion about Ward identities are performed.In the second part, the attention is centered on statistical mechanics but with an approach typical of field theory, in particular, focused to the study of classical and quantum phase transitions from the quantized version of the spherical model and its supersymmetric extension.
This volume contains the lectures delivered at the XIV Training Course in the Physics of Strongly Correlated Systems, held in Vietri sul Mare (Salerno) Italy, in October 2009. The project of the meeting was to promote the formation of young scientists by means of training through research. These features are reflected in the book: the lectures are up-to-date monographs of relevant subjects in the field of Condensed Matter Physics. Contributions include: Electronic Structure of Strongly Correlated Materials (Electronic structure calculations in one-electron approximation; Hubbard model in Dynamical Mean-Field Theory (DMFT); Electronic structure calculations for real materials by LDA+DMFT method); and, Computational Studies of Quantum Spin Systems (Quantum spin models, their ground states and quantum phase transitions; Classical phase transitions, Monte Carlo simulations, and finite-size scaling; Exact diagonalization methods; Quantum Monte Carlo simulations and the Stochastic Series Expansion method; and, Survey of related computational methods). Contributions also include: Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials (Mean-field theories for many-body systems; Lattice fermions in the limit of high dimensions; Dynamical mean-field theory for correlated lattice fermions; The Mott-Hubbard Metal-Insulator Transition; Electronic correlations and disorder; Theory of electronic correlations in materials; and, Kinks in the dispersion of strongly correlated electron systems).
From July 21 to August 9, 1958, a summer course on Mathematical Problems of Quantum Theory of Particles and Fields was held in Varenna, Italy. The lectures took place in the Villa Monastero, on the shores of beautiful Lake Como; the place is well known to the readers of Physics Today since in other issues (Dec. 1957, Jan. 1958) there have been reports about conferences held there, and about other courses of the International School of Physics. The school is organized by the Italian Physical Society and is sponsored by the Italian National Science Council, by the Italian Government, by some Italian universities, by various local representatives, and occasionally by other institutions. Each summer it gives a number of courses (recently three or four), on special topics in physics. These courses are neither meetings of experts, nor quick courses at the graduate-school level. The goal is to put the persons with most experience in a field in touch with the younger or less experienced, in order to give the latter an up-to-date picture of recent research and open problems. The courses are organized quite independently and vary in length from a few days to three weeks in the present case.