Quantum Monte Carlo Methods In Condensed Matter Physics

Masuo Suzuki

• Publisher: World Scientific
• Year: 1993
• ISBN:
  9789814503815
• Topic: Sciences physiques
• Subtopic: Astronomie et astrophysique

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-Tc 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.

Table of contents

• CONTENTS
• PREFACE
• GENERAL DECOMPOSITION THEORY OF EXPONENTIAL OPERATORS
• QUANTUM MONTE CARLO AND RELATED METHODS— RECENT DEVELOPMENTS —
• MONTE CARLO RENORMALIZATION GROUP STUDY OF THE D=l XXZ MODEL
• OVERCOMING CRITICAL SLOWING DOWN IN QUANTUM MONTE CARLO SIMULATIONS
• QUANTUM MANYBODY SPIN SYSTEMS IN RANDOM FIELDS AND ANKOTROPIES
• INHOMOGENEITY EFFECTS IN QUANTUM SPIN SYSTEMS
• THE QUANTUM TRANSFER MATRIX AND ITS APPLICATION TO QUANTUM SPIN CHAINS
• TRANSFER MATRICES IN QUANTUM MANY-BODY SYSTEMS
• MONTE CARLO CALCULATIONS OF ELEMENTARY EXCITATION
• THE DECOUPLED CELL METHOD OF QUANTUM MONTE CARLO CALCULATION
• Decoupled Cell Monte Carlo Study of the Critical Properties of the Spin-1/2 Ferromagnetic Heisenberg Model in Three Dimensions
• VARIATIONAL MONTE CARLO STUDIES OF CORRELATED ELECTRONS
• QUANTUM MONTE CARLO SIMULATION OF MULTIBAND FERMION SYSTEMS AND ITS APPLICATION TO SUPERCONDUCTIVITY
• QUANTUM MONTE CARLO IN THE INFINITE DIMENSIONAL LIMIT
• ASPECTS OF THE SIGN PROBLEM
• QUANTUM SIMULATIONS OF THE DEGENERATE SINGLE-IMPURITY ANDERSON MODEL
• QUANTUM MONTE CAR^O SIMULATION BY AUXILIARY FIELDS
• GROUND-STATE PROJECTION USING AUXILIARY FIELDS
• FERMION SIMULATIONS OF CORRELATED SYSTEMS
• DIRTY BOSONS IN 2D: PHASES AND PHASE TRANSITIONS
• PATH-INTEGRAL QUANTUM MONTE CARLO STUDIES OF THE STATIC AND TIME-DEPENDENT THERMODYNAMICS OF THE VIBRATIONAL PROPERTIES OF CRYSTALS
• RELAXATION OF QUANTUM SYSTEMS IN FLUCTUATING MEDIA