Quantum Monte Carlo Approaches for Correlated Systems

Quantum Monte Carlo Approaches for Correlated Systems
Author: Federico Becca
Publisher: Cambridge University Press
Total Pages: 287
Release: 2017-11-30
Genre: Science
ISBN: 1108547311

Over the past several decades, computational approaches to studying strongly-interacting systems have become increasingly varied and sophisticated. This book provides a comprehensive introduction to state-of-the-art quantum Monte Carlo techniques relevant for applications in correlated systems. Providing a clear overview of variational wave functions, and featuring a detailed presentation of stochastic samplings including Markov chains and Langevin dynamics, which are developed into a discussion of Monte Carlo methods. The variational technique is described, from foundations to a detailed description of its algorithms. Further topics discussed include optimisation techniques, real-time dynamics and projection methods, including Green's function, reptation and auxiliary-field Monte Carlo, from basic definitions to advanced algorithms for efficient codes, and the book concludes with recent developments on the continuum space. Quantum Monte Carlo Approaches for Correlated Systems provides an extensive reference for students and researchers working in condensed matter theory or those interested in advanced numerical methods for electronic simulation.

Theoretical Methods for Strongly Correlated Electrons

Theoretical Methods for Strongly Correlated Electrons
Author: David Sénéchal
Publisher: Springer Science & Business Media
Total Pages: 370
Release: 2006-05-09
Genre: Science
ISBN: 0387217177

Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type - i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions.

Quantum Monte Carlo Approaches for Correlated Systems

Quantum Monte Carlo Approaches for Correlated Systems
Author: Federico Becca
Publisher: Cambridge University Press
Total Pages: 287
Release: 2017-11-30
Genre: Mathematics
ISBN: 1107129931

A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems. Including variational wave functions, stochastic samplings, the variational technique, optimisation techniques, real-time dynamics and projection methods and recent developments on the continuum space. An extensive resource for students and researchers.

Strongly Correlated Systems

Strongly Correlated Systems
Author: Adolfo Avella
Publisher: Springer Science & Business Media
Total Pages: 350
Release: 2013-04-05
Genre: Science
ISBN: 3642351069

This volume presents, for the very first time, an exhaustive collection of those modern numerical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and material science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciate consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.

Quantum Monte Carlo Methods in Condensed Matter Physics

Quantum Monte Carlo Methods in Condensed Matter Physics
Author: Masuo Suzuki
Publisher: World Scientific
Total Pages: 380
Release: 1993
Genre: Science
ISBN: 9789810236830

This book reviews recent developments of quantum Monte Carlo methods and some remarkable applications to interacting quantum spin systems and strongly correlated electron systems. It contains twenty-two papers by thirty authors. Some of the features are as follows. The first paper gives the foundations of the standard quantum Monte Carlo method, including some recent results on higher-order decompositions of exponential operators and ordered exponentials. The second paper presents a general review of quantum Monte Carlo methods used in the present book. One of the most challenging problems in the field of quantum Monte Carlo techniques, the negative-sign problem, is also discussed and new methods proposed to partially overcome it. In addition, low-dimensional quantum spin systems are studied. Some interesting applications of quantum Monte Carlo methods to fermion systems are also presented to investigate the role of strong correlations and fluctuations of electrons and to clarify the mechanism of high-c superconductivity. Not only thermal properties but also quantum-mechanical ground-state properties have been studied by the projection technique using auxiliary fields. Further, the Haldane gap is confirmed by numerical calculations. Active researchers in the forefront of condensed matter physics as well as young graduate students who want to start learning the quantum Monte Carlo methods will find this book useful.

Neural-Network Simulation of Strongly Correlated Quantum Systems

Neural-Network Simulation of Strongly Correlated Quantum Systems
Author: Stefanie Czischek
Publisher: Springer Nature
Total Pages: 212
Release: 2020-08-27
Genre: Science
ISBN: 3030527158

Quantum systems with many degrees of freedom are inherently difficult to describe and simulate quantitatively. The space of possible states is, in general, exponentially large in the number of degrees of freedom such as the number of particles it contains. Standard digital high-performance computing is generally too weak to capture all the necessary details, such that alternative quantum simulation devices have been proposed as a solution. Artificial neural networks, with their high non-local connectivity between the neuron degrees of freedom, may soon gain importance in simulating static and dynamical behavior of quantum systems. Particularly promising candidates are neuromorphic realizations based on analog electronic circuits which are being developed to capture, e.g., the functioning of biologically relevant networks. In turn, such neuromorphic systems may be used to measure and control real quantum many-body systems online. This thesis lays an important foundation for the realization of quantum simulations by means of neuromorphic hardware, for using quantum physics as an input to classical neural nets and, in turn, for using network results to be fed back to quantum systems. The necessary foundations on both sides, quantum physics and artificial neural networks, are described, providing a valuable reference for researchers from these different communities who need to understand the foundations of both.

Quantum Monte Carlo Methods

Quantum Monte Carlo Methods
Author: James Gubernatis
Publisher: Cambridge University Press
Total Pages: 503
Release: 2016-06-02
Genre: Science
ISBN: 1316483126

Featuring detailed explanations of the major algorithms used in quantum Monte Carlo simulations, this is the first textbook of its kind to provide a pedagogical overview of the field and its applications. The book provides a comprehensive introduction to the Monte Carlo method, its use, and its foundations, and examines algorithms for the simulation of quantum many-body lattice problems at finite and zero temperature. These algorithms include continuous-time loop and cluster algorithms for quantum spins, determinant methods for simulating fermions, power methods for computing ground and excited states, and the variational Monte Carlo method. Also discussed are continuous-time algorithms for quantum impurity models and their use within dynamical mean-field theory, along with algorithms for analytically continuing imaginary-time quantum Monte Carlo data. The parallelization of Monte Carlo simulations is also addressed. This is an essential resource for graduate students, teachers, and researchers interested in quantum Monte Carlo techniques.

Effective Models for Low-Dimensional Strongly Correlated Systems

Effective Models for Low-Dimensional Strongly Correlated Systems
Author: Ghassan George Batrouni
Publisher: Springer Science & Business Media
Total Pages: 340
Release: 2006-02-23
Genre: Science
ISBN: 9780735403093

These proceedings cover the most recent developments in the fields of high temperature superconductivity, magnetic materials and cold atoms in traps. Special emphasis is given to recently developed numerical and analytical methods, such as effective model Hamiltonians, density matrix renormalization group as well as quantum Monte Carlo simulations. Several of the contributions are written by the pioneers of these methods.

Computer Simulation Studies in Condensed-Matter Physics XII

Computer Simulation Studies in Condensed-Matter Physics XII
Author: D. P. Landau
Publisher: Springer Science & Business Media
Total Pages: 238
Release: 2012-12-06
Genre: Science
ISBN: 3642596894

More than a decade ago, because of the phenomenal growth in the power of computer simulations, The University of Georgia formed the first institutional unit devoted to the use of simulations in research and teaching: The Center for Simulational Physics. As the simulations community expanded further, we sensed a need for a meeting place for both experienced simulators and neophytes to discuss new techniques and recent results in an environment which promoted extended discussion. As a consequence, the Center for Sim ulational Physics established an annual workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics. This year's workshop was the twelfth in this series. It was held at The University of Geor gia, March 8-12, 1999 as an unofficial satellite conference to the Centennial Meeting of the American Physical Society in Atlanta, GA. The continued interest shown by the scientific community demonstrates quite clearly the useful purpose which the series has served. These proceedings provide a "sta tus report" on a number of important topics. This volume is published with the goal of timely dissemination of the material to a wider audience. We wish to offer special thanks to IBM Corporation for their generous support of this year's workshop. This volume contains both invited papers and contributed presentations on problems in both classical and quantum condensed matter physics. We hope that each reader will benefit from specialized results as well as profit from exposure to new algorithms, methods of analysis, and conceptual devel opments.