Geometrically Constructed Markov Chain Monte Carlo Study Of Quantum Spin Phonon Complex Systems
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Geometrically Constructed Markov Chain Monte Carlo Study Of Quantum Spin Phonon Complex Systems
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Author : Hidemaro Suwa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-05
Geometrically Constructed Markov Chain Monte Carlo Study Of Quantum Spin Phonon Complex Systems written by Hidemaro Suwa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-05 with Science categories.
In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the spin-Peierls systems. Three significant methods are introduced for the first time: a new optimization algorithm of the Markov chain transition kernel based on the geometric weight-allocation approach, the extension of the worm (directed-loop) algorithm to nonconserved particles, and the combination with the level spectroscopy. Utilizing these methods, the phase diagram of the one-dimensional XXZ spin-Peierls system is elucidated. Furthermore, the multi-chain and two-dimensional spin-Peierls systems with interchain lattice interaction are investigated. The unbiased simulation shows that the interesting quantum phase transition between the 1D-like liquid phase and the macroscopically-degenerated dimer phase occurs on the fully-frustrated parameter line that separates the doubly-degenerated dimer phases in the two-dimensional phase diagram. The spin-phonon interaction in the spin-Peierls system introduces the spin frustration, which usually hinders the quantum Monte Carlo analysis, owing to the notorious negative sign problem. In this thesis, the author has succeeded in precisely calculating the critical phenomena of the effectively frustrated quantum spin system by means of the quantum Monte Carlo method without the negative sign.
Magnetic Field Effects In Low Dimensional Quantum Magnets
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Author : Adam Iaizzi
language : en
Publisher: Springer
Release Date : 2018-11-28
Magnetic Field Effects In Low Dimensional Quantum Magnets written by Adam Iaizzi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Science categories.
This thesis is a tour-de-force combination of analytic and computational results clarifying and resolving important questions about the nature of quantum phase transitions in one- and two-dimensional magnetic systems. The author presents a comprehensive study of a low-dimensional spin-half quantum antiferromagnet (the J-Q model) in the presence of a magnetic field in both one and two dimensions, demonstrating the causes of metamagnetism in such systems and providing direct evidence of fractionalized excitations near the deconfined quantum critical point. In addition to describing significant new research results, this thesis also provides the non-expert with a clear understanding of the nature and importance of computational physics and its role in condensed matter physics as well as the nature of phase transitions, both classical and quantum. It also contains an elegant and detailed but accessible summary of the methods used in the thesis—exact diagonalization, Monte Carlo, quantum Monte Carlo and the stochastic series expansion—that will serve as a valuable pedagogical introduction to students beginning in this field.
Journal Of The Physical Society Of Japan
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Author :
language : en
Publisher:
Release Date : 2017
Journal Of The Physical Society Of Japan written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Physics categories.
A Guide To Monte Carlo Simulations In Statistical Physics
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Author : David P. Landau
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-17
A Guide To Monte Carlo Simulations In Statistical Physics written by David P. Landau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-17 with Mathematics categories.
This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader.
Emergent Phenomena In Correlated Matter
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Author : Eva Pavarini
language : en
Publisher: Forschungszentrum Jülich
Release Date : 2013
Emergent Phenomena In Correlated Matter written by Eva Pavarini and has been published by Forschungszentrum Jülich this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Statistical Mechanics Algorithms And Computations
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Author : Werner Krauth
language : en
Publisher: OUP Oxford
Release Date : 2006-09-14
Statistical Mechanics Algorithms And Computations written by Werner Krauth and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-14 with Science categories.
This book discusses the computational approach in modern statistical physics in a clear yet accessible way, and works out its intimate relations with other approaches in theoretical physics. Individual chapters focus on subjects as diverse as the hard sphere liquid, classical spin models, single quantum particles and Bose-Einstein condensation. They contain in-depth discussions of algorithms ranging from basic enumeration methods to modern Monte Carlo techniques. The emphasis is on orientation. Discussions of implementation details are kept to a minimum. The book heavily relies on illustrations, tables and concise printed algorithms to convey key information: all the material remains easily accessible. The book is fully self-contained: graphs and tables can be readily reproduced by programming at most a few dozen lines of computer code. Most sections lead from an elementary discussion to the rich and difficult problems of contemporary computational and statistical physics, and will be of interest to a wide range of students, teachers and researchers in physics and the neighboring sciences. An accompanying CD allows to incorporate the layout material (illustrations, tables, schematic programs) into the reader's own presentations.
Markov Chain Monte Carlo Simulations And Their Statistical Analysis
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Author : Bernd A. Berg
language : en
Publisher: World Scientific
Release Date : 2004
Markov Chain Monte Carlo Simulations And Their Statistical Analysis written by Bernd A. Berg and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
This book teaches modern Markov chain Monte Carlo (MC) simulation techniques step by step. The material should be accessible to advanced undergraduate students and is suitable for a course. It ranges from elementary statistics concepts (the theory behind MC simulations), through conventional Metropolis and heat bath algorithms, autocorrelations and the analysis of the performance of MC algorithms, to advanced topics including the multicanonical approach, cluster algorithms and parallel computing. Therefore, it is also of interest to researchers in the field. The book relates the theory directly to Web-based computer code. This allows readers to get quickly started with their own simulations and to verify many numerical examples easily. The present code is in Fortran 77, for which compilers are freely available. The principles taught are important for users of other programming languages, like C or C++.
The Nonlinear World
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Author : Yoshitsugu Oono
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-30
The Nonlinear World written by Yoshitsugu Oono and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Science categories.
The most important characteristic of the “world filled with nonlinearity” is the existence of scale interference: disparate space–time scales interfere with each other. Thus, the effects of unknowable scales invade the world that we can observe directly. This leads to various peculiar phenomena such as chaos, critical phenomena, and complex biological phenomena, among others. Conceptual analysis and phenomenology are the keys to describe and understand phenomena that are subject to scale interference, because precise description of unfamiliar phenomena requires precise concepts and their phenomenological description. The book starts with an illustration of conceptual analysis in terms of chaos and randomness, and goes on to explain renormalization group philosophy as an approach to phenomenology. Then, abduction is outlined as a way to express what we have understood about the world. The book concludes with discussions on how we can approach genuinely complex phenomena, including biological phenomena. The main target of this volume is young people who have just started to appreciate the world seriously. The author also wishes the book to be helpful to those who have been observing the world, but who wish to appreciate it afresh from a different angle.
Theoretical Methods For Strongly Correlated Electrons
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Author : David Sénéchal
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-09
Theoretical Methods For Strongly Correlated Electrons written by David Sénéchal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-09 with Science categories.
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.
Machine Learning Meets Quantum Physics
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Author : Kristof T. Schütt
language : en
Publisher: Springer Nature
Release Date : 2020-06-03
Machine Learning Meets Quantum Physics written by Kristof T. Schütt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-03 with Science categories.
Designing molecules and materials with desired properties is an important prerequisite for advancing technology in our modern societies. This requires both the ability to calculate accurate microscopic properties, such as energies, forces and electrostatic multipoles of specific configurations, as well as efficient sampling of potential energy surfaces to obtain corresponding macroscopic properties. Tools that can provide this are accurate first-principles calculations rooted in quantum mechanics, and statistical mechanics, respectively. Unfortunately, they come at a high computational cost that prohibits calculations for large systems and long time-scales, thus presenting a severe bottleneck both for searching the vast chemical compound space and the stupendously many dynamical configurations that a molecule can assume. To overcome this challenge, recently there have been increased efforts to accelerate quantum simulations with machine learning (ML). This emerging interdisciplinary community encompasses chemists, material scientists, physicists, mathematicians and computer scientists, joining forces to contribute to the exciting hot topic of progressing machine learning and AI for molecules and materials. The book that has emerged from a series of workshops provides a snapshot of this rapidly developing field. It contains tutorial material explaining the relevant foundations needed in chemistry, physics as well as machine learning to give an easy starting point for interested readers. In addition, a number of research papers defining the current state-of-the-art are included. The book has five parts (Fundamentals, Incorporating Prior Knowledge, Deep Learning of Atomistic Representations, Atomistic Simulations and Discovery and Design), each prefaced by editorial commentary that puts the respective parts into a broader scientific context.