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Quantum Monte Carlo Study Of One Dimensional Bosons With Finite Range Interactions
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Book Synopsis Quantum Monte Carlo Study of One-dimensional Bosons with Finite Range Interactions by : Víctor Camí Núñez
Download or read book Quantum Monte Carlo Study of One-dimensional Bosons with Finite Range Interactions written by Víctor Camí Núñez and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We have studied how the ground state and the one-body density distribution of a one-dimensional system of bosons trapped by a harmonic oscillator potential depend on the repulsive interaction between the bosons. This study has been done using two numerical methods: Variational Monte Carlo and Diffusion Monte Carlo to retrieve information about the ground state energy and the one-body density distribution. We have covered the full range of interaction from the non-interacting regime, where the mean field approximation is a suitable way to describe our system, to the strongly interacting regime where we have reproduced approximately the behavior of a Tonks-Girardeau gas. As the repulsive interaction strength is increased, the system builds pair correlations. We have also proposed a correlated wave function to characterise these correlations.
Book Synopsis Quantum Monte Carlo Methods in Condensed Matter Physics by : Masuo Suzuki
Download or read book Quantum Monte Carlo Methods in Condensed Matter Physics written by Masuo Suzuki and published by World Scientific. This book was released on 1993 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Monte Carlo Methods in Physics and Chemistry by : M.P. Nightingale
Download or read book Quantum Monte Carlo Methods in Physics and Chemistry written by M.P. Nightingale and published by Springer Science & Business Media. This book was released on 1998-12-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been a considerable growth in interest in Monte Carlo methods, and quantum Monte Carlo methods in particlular. Clearly, the ever-increasing computational power available to researchers, has stimulated the development of improved algorithms, and almost all fields in computational physics and chemistry are affected by their applications. Here we just mention some fields that are covered in the lecture notes contained in this volume, viz. electronic structure studies of atoms, molecules and solids, nuclear structure, and low- or zero-temperature studies of strongly-correlated quantum systems, both of the continuum and lattice variety, and cooperative phenomena in classical systems. Although each area of application may have its own peculiarities, requiring specialized solutions, all share the same basic methodology. It was with the intention of bringing together researchers and students from these various areas that the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry was held at Cornell University from 12 to 24 July, 1998. This book contains material presented at the Institute in a series of mini courses in quantum Monte Carlo methods. The program consisted of lectures predominantly of a pedagogical nature, and of more specialized seminars. The levels varied from introductory to advanced, and from basic methods to applications; the program was intended for an audience working towards the Ph.D. level and above. Despite the essentially pedagogic nature of the Institute, several of the lectures and seminars contained in this volume present recent developments not previously published.
Book Synopsis Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems by : Hidemaro Suwa
Download or read book Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems written by Hidemaro Suwa and published by Springer Science & Business Media. This book was released on 2013-11-05 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Monte Carlo Simulations of Ultracold Bosons in a Double Well by : Joel Christopher Corbo
Download or read book Quantum Monte Carlo Simulations of Ultracold Bosons in a Double Well written by Joel Christopher Corbo and published by . This book was released on 2013 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present path integral ground state (PIGS) quantum Monte Carlo calculations for the ground state (T = 0) properties of repulsively interacting bosons in a three-dimensional external double well potential over a range of interaction strengths and potential parameters. We focus our calculations on ground state number statistics and the one-body density matrix in order to understand the level of squeezing and fragmentation that the system exhibits as a function of interaction strength, and we compare our PIGS results to both a standard and an improved two-mode model and a recently-proposed eight-mode model. In general, the various models agree with the PIGS simulations for weak interactions, but the full quantum Monte Carlo treatment is required to correctly predict the amount of squeezing and fragmentation exhibited for strong interactions. One novel and somewhat surprising result from our simulations involves the relationship between squeezing and interaction strength: rather than a monotonic relationship between these quantities, we find that for certain double well barrier heights the squeezing increases as a function of interaction strength until it reaches a maximum, after which it decreases again. We also see a similar relationship between fragmentation and interaction strength. We propose novel physical mechanisms to account for this behavior.
Book Synopsis An Introduction to Quantum Monte Carlo Methods by : Tao Pang
Download or read book An Introduction to Quantum Monte Carlo Methods written by Tao Pang and published by Morgan & Claypool Publishers. This book was released on 2016-12-07 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been very prominent in computer simulation of various systems in physics, chemistry, biology, and materials science. This book focuses on the discussion and path-integral quantum Monte Carlo methods in many-body physics and provides a concise but complete introduction to the Metropolis algorithm and its applications in these two techniques. To explore the schemes in clarity, several quantum many-body systems are analysed and studied in detail. The book includes exercises to help digest the materials covered. It can be used as a tutorial to learn the discussion and path-integral Monte Carlo or a recipe for developing new research in the reader's own area. Two complete Java programs, one for the discussion Monte Carlo of 4^He clusters on a graphite surface and the other for the path-integral Monte Carlo of cold atoms in a potential trap, are ready for download and adoption.
Book Synopsis Universal Themes of Bose-Einstein Condensation by : Nick P. Proukakis
Download or read book Universal Themes of Bose-Einstein Condensation written by Nick P. Proukakis and published by Cambridge University Press. This book was released on 2017-04-27 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following an explosion of research on Bose–Einstein condensation (BEC) ignited by demonstration of the effect by 2001 Nobel prize winners Cornell, Wieman and Ketterle, this book surveys the field of BEC studies. Written by experts in the field, it focuses on Bose–Einstein condensation as a universal phenomenon, covering topics such as cold atoms, magnetic and optical condensates in solids, liquid helium and field theory. Summarising general theoretical concepts and the research to date - including novel experimental realisations in previously inaccessible systems and their theoretical interpretation - it is an excellent resource for researchers and students in theoretical and experimental physics who wish to learn of the general themes of BEC in different subfields.
Book Synopsis Quantum Monte Carlo by : James B. Anderson
Download or read book Quantum Monte Carlo written by James B. Anderson and published by OUP USA. This book was released on 2007-04-05 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and straightforward and rooted in statistics and probability theory, their defining characteristic being that the methodology relies on random or pseudo-random sequences of numbers. It is a technique of numerical analysis based on the approximate solution of a problem using repeated sampling experiments and observing the proportion of times a given property is satisfied. The term Monte Carlo was first used to describe calculational methods based on chance in the 1940s, but the methods themselves preceded the term by as much as a century. Quantum Monte Carlo (QMC) first appeared in 1982 and similarly was preceded by development of the related calculational methodology. The success of QMC methods over the past few decades has been remarkable, and this book will clearly demonstrate that success in its discussion of applications. For isolated molecules, the basic material of chemistry, QMC methods have produced exact solutions of the Schroedinger equation for very small systems and the most accurate solutions available for very large systems. The range of applications is impressive: folding of protein molecules, interactions in liquids, structure modeling in crystals and enzymes, quantum dots, designing heat shields and aerodynamic forms, architecture, design, business and economics, and even cinema and video games (3D modeling). This book takes a similar approach to Henry Schaefers classic book Quantum Chemistry (OUP, 1984 now a Dover edition), collecting summaries of some of the most important papers in the quantum Monte Carlo literature, tying everything together with analysis and discussion of applications. Quantum Monte Carlo is a reference book for quantum Monte Carlo applications, belonging near the desk of every quantum chemist, physicist, and a wide range of scientists and engineers across many disciplines, destined to become a classic.
Book Synopsis Quantum Monte Carlo Methods by : James Gubernatis
Download or read book Quantum Monte Carlo Methods written by James Gubernatis and published by Cambridge University Press. This book was released on 2016-06-02 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis New Theoretical Approaches to Strongly Correlated Systems by : Alexei M. Tsvelik
Download or read book New Theoretical Approaches to Strongly Correlated Systems written by Alexei M. Tsvelik and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: For many years, the physics of strongly correlated systems was considered a theorists' playground, right at the border with pure mathematics, where physicists from the `real world' did not venture. The time has come, however, when healthy physics cannot exist without these techniques and results. Lectures on selected topics in the theory of strongly correlated systems are here presented by the leading experts in the field. Topics covered include a use of the form factor approach in low-dimensional systems, applications of quantum field theory to disorder, and dynamical mean field theory. The main divisions of the book deal with: I) Quantum Critical Points; (II) Strongly Correlated One-Dimensional Systems; (III) Strong Correlations and Disorder; and (IV) Dynamical Mean Field Theory.
Book Synopsis Monte Carlo Methods in Quantum Problems by : M.H. Kalos
Download or read book Monte Carlo Methods in Quantum Problems written by M.H. Kalos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been a tool of theoretical and computational scientists for many years. In particular, the invention and percolation of the algorithm of Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller sparked a rapid growth of applications to classical statistical mechanics. Although proposals for treatment of quantum systems had been made even earlier, only a few serious calculations had heen carried out. Ruch calculations are generally more consuming of computer resources than for classical systems and no universal algorithm had--or indeed has yet-- emerged. However, with advances in techniques and in sheer computing power, Monte Carlo methods have been used with considerable success in treating quantum fluids and crystals, simple models of nuclear matter, and few-body nuclei. Research at several institutions suggest that they may offer a new approach to quantum chemistry, one that is independent of basis ann yet capable of chemical accuracy. That. Monte Carlo methods can attain the very great precision needed is itself a remarkable achievement. More recently, new interest in such methods has arisen in two new a~as. Particle theorists, in particular K. Wilson, have drawn attention to the rich analogy between quantum field theoty and statistical mechanics and to the merits of Monte Carlo calculations for lattice gauge theories. This has become a rapidly growing sub-field. A related development is associated with lattice problems in quantum physics, particularly with models of solid state systems. The~ is much ferment in the calculation of various one-dimensional problems such as the'Hubbard model.
Book Synopsis Quantum Monte Carlo Approaches for Correlated Systems by : Federico Becca
Download or read book Quantum Monte Carlo Approaches for Correlated Systems written by Federico Becca and published by Cambridge University Press. This book was released on 2017-11-30 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Gas Experiments: Exploring Many-body States by : Paivi Torma
Download or read book Quantum Gas Experiments: Exploring Many-body States written by Paivi Torma and published by World Scientific. This book was released on 2014-09-16 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum phenomena of many-particle systems are fascinating in their complexity and are consequently not fully understood and largely untapped in terms of practical applications. Ultracold gases provide a unique platform to build up model systems of quantum many-body physics with highly controlled microscopic constituents. In this way, many-body quantum phenomena can be investigated with an unprecedented level of precision, and control and models that cannot be solved with present day computers may be studied using ultracold gases as a quantum simulator.This book addresses the need for a comprehensive description of the most important advanced experimental methods and techniques that have been developed along with the theoretical framework in a clear and applicable format. The focus is on methods that are especially crucial in probing and understanding the many-body nature of the quantum phenomena in ultracold gases and most topics are covered both from a theoretical and experimental viewpoint, with interrelated chapters written by experts from both sides of research.Graduate students and post-doctoral researches working on ultracold gases will benefit from this book, as well as researchers from other fields who wish to gain an overview of the recent fascinating developments in this very dynamically evolving field. Sufficient level of both detailed high level research and a pedagogical approach is maintained throughout the book so as to be of value to those entering the field as well as advanced researchers. Furthermore, both experimentalists and theorists will benefit from the book; close collaboration between the two are continuously driving the field to a very high level and will be strengthened to continue the important progress yet to be made in the field.
Book Synopsis Quantum Phase Transitions in Transverse Field Spin Models by : Amit Dutta
Download or read book Quantum Phase Transitions in Transverse Field Spin Models written by Amit Dutta and published by Cambridge University Press. This book was released on 2015-01-28 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: The transverse field Ising and XY models (the simplest quantum spin models) provide the organising principle for the rich variety of interconnected subjects which are covered in this book. From a generic introduction to in-depth discussions of the subtleties of the transverse field Ising and related models, it includes the essentials of quantum dynamics and quantum information. A wide range of relevant topics has also been provided: quantum phase transitions, various measures of quantum information, the effects of disorder and frustration, quenching dynamics and the Kibble–Zurek scaling relation, the Kitaev model, topological phases of quantum systems, and bosonisation. In addition, it also discusses the experimental studies of transverse field models (including the first experimental realisation of quantum annealing) and the recent realisation of the transverse field Ising model using tunable Josephson junctions. Further, it points to the obstacles still remaining to develop a successful quantum computer.
Book Synopsis Recent Progress in Many-body Theories by : Jordi Boronat
Download or read book Recent Progress in Many-body Theories written by Jordi Boronat and published by World Scientific. This book was released on 2008 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the main contributions to the 14th International Conference on Recent Progress in Many-Body Theories (RPMBT14) held at the Technical University of Catalonia, Spain, in July 2007. This conference, which was first held in Trieste in 1979, is devoted to new developments in the field of many-body theories, which are being applied and developed in a rapidly growing number of fields. The emphasis is twofold: progress in the technical aspects of microscopic theories and a review of recent applications of many-body techniques. In addition to the more traditional topics, such as nuclear physics and quantum liquids, the present volume also includes the most recent results on atomic physics, cold Bose and Fermi gases, phase transitions and quantum information. Moreover, the volume contains the lectures of the winners of the 2007 Feenberg Medal and 2007 Kuemmel Award, as well as their laudatios.
Book Synopsis Statistical Mechanics: Algorithms and Computations by : Werner Krauth
Download or read book Statistical Mechanics: Algorithms and Computations written by Werner Krauth and published by Oxford University Press, USA. This book was released on 2006-09-14 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the computational approach in modern statistical physics in a clear and accessible way and demonstrates its close relation to 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. Contained within the chapters are in-depth discussions of algorithms, ranging from basic enumeration methods to modern Monte Carlo techniques. The emphasis is on orientation, with discussion of implementation details kept to a minimum. Illustrations, tables and concise printed algorithms convey key information, making the material very accessible. The book is completely self-contained and graphs and tables can readily be reproduced, requiring minimal computer code. Most sections begin at an elementary level and lead on to the rich and difficult problems of contemporary computational and statistical physics. The book will be of interest to a wide range of students, teachers and researchers in physics and the neighbouring sciences. An accompanying CD allows incorporation of the book's content (illustrations, tables, schematic programs) into the reader's own presentations.
Book Synopsis Quantum Monte Carlo Studies of Strongly Interacting Fermionic Systems by : Lucas Madeira
Download or read book Quantum Monte Carlo Studies of Strongly Interacting Fermionic Systems written by Lucas Madeira and published by . This book was released on 2018 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation two kinds of strongly interacting fermionic systems were studied: cold atomic gases and nucleon systems. In the first part I report T=0 diffusion Monte Carlo results for the ground-state and vortex excitation of unpolarized spin-1/2 fermions in a two-dimensional disk. I investigate how vortex core structure properties behave over the BEC-BCS crossover. The vortex excitation energy, density profiles, and vortex core properties related to the current are calculated. A density suppression at the vortex core on the BCS side of the crossover and a depleted core on the BEC limit is found. Size-effect dependencies in the disk geometry were carefully studied. In the second part of this dissertation I turn my attention to a very interesting problem in nuclear physics. In most simulations of nonrelativistic nuclear systems, the wave functions are found by solving the many-body Schrödinger equations, and they describe the quantum-mechanical amplitudes of the nucleonic degrees of freedom. In those simulations the pionic contributions are encoded in nuclear potentials and electroweak currents, and they determine the low-momentum behavior. By contrast, in this work I present a novel quantum Monte Carlo formalism in which both relativistic pions and nonrelativistic nucleons are explicitly included in the quantum-mechanical states of the system. I report the renormalization of the nucleon mass as a function of the momentum cutoff, an Euclidean time density correlation function that deals with the short-time nucleon diffusion, and the pion cloud density and momentum distributions. In the two nucleon sector the interaction of two static nucleons at large distances reduces to the one-pion exchange potential, and I fit the low-energy constants of the contact interactions to reproduce the binding energy of the deuteron and two neutrons in finite volumes. I conclude by showing that the method can be readily applied to light-nuclei.
