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Quantum Monte Carlo Approaches for Correlated Systems [Kõva köide]

, (Scuola Internazionale Superiore di Studi Avanzati, Trieste)
  • Formaat: Hardback, 286 pages, kõrgus x laius x paksus: 254x179x16 mm, kaal: 710 g, 3 Tables, black and white; 5 Halftones, black and white; 26 Line drawings, black and white
  • Ilmumisaeg: 30-Nov-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107129931
  • ISBN-13: 9781107129931
Teised raamatud teemal:
Quantum Monte Carlo Approaches for Correlated SystemsSuurem pilt
  • Formaat: Hardback, 286 pages, kõrgus x laius x paksus: 254x179x16 mm, kaal: 710 g, 3 Tables, black and white; 5 Halftones, black and white; 26 Line drawings, black and white
  • Ilmumisaeg: 30-Nov-2017
  • Kirjastus: Cambridge University Press
  • ISBN-10: 1107129931
  • ISBN-13: 9781107129931
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781107129931.html
Märksõnad:
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.

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.

Muu info

A comprehensive introduction to state-of-the-art quantum Monte Carlo techniques for applications in strongly-interacting systems including a presentation of stochastic samplings.
Preface ix
Acknowledgements xii
Part I Introduction
1(36)
1 Correlated Models and Wave Functions
3(34)
1.1 Introduction
3(3)
1.2 The Matrix Formulation
6(1)
1.3 Effective Lattice Models
7(6)
1.4 The Variational Principle
13(1)
1.5 Variational Wave Functions
14(17)
1.6 Size Extensivity
31(3)
1.7 Projection Techniques
34(3)
Part II Probability and Sampling
37(64)
2 Probability Theory
39(17)
2.1 Introduction
39(2)
2.2 Events and Probability
41(3)
2.3 Moments of the Distribution: Mean Value and Variance
44(3)
2.4 Changing Random Variables
47(1)
2.5 The Chebyshev's Inequality
48(1)
2.6 Summing Independent Random Variables
48(5)
2.7 The Central Limit Theorem
53(3)
3 Monte Carlo Sampling and Markov Chains
56(29)
3.1 Introduction
56(3)
3.2 Reweighting Technique and Correlated Sampling
59(1)
3.3 Direct Sampling
60(1)
3.4 Importance Sampling
61(1)
3.5 Sampling a Discrete Distribution Probability
62(2)
3.6 Sampling a Continuous Density Probability
64(2)
3.7 Markov Chains
66(3)
3.8 Detailed Balance and Approach to Equilibrium
69(5)
3.9 Metropolis Algorithm
74(2)
3.10 How to Estimate Errorbars
76(6)
3.11 Errorbars in Correlated Samplings
82(3)
4 Langevin Molecular Dynamics
85(16)
4.1 Introduction
85(2)
4.2 Discrete-Time Langevin Dynamics
87(2)
4.3 From the Langevin to the Fokker-Planck Equation
89(2)
4.4 Fokker-Planck Equation and Quantum Mechanics
91(5)
4.5 Accelerated Langevin Dynamics
96(5)
Part III Variational Monte Carlo
101(64)
5 Variational Monte Carlo
103(28)
5.1 Quantum Averages and Statistical Samplings
103(2)
5.2 The Zero-Variance Property
105(1)
5.3 Jastrow and Jastrow-Slater Wave Functions
106(2)
5.4 The Choice of the Basis Sets
108(1)
5.5 Bosonic Systems
109(3)
5.6 Fermionic Systems with Determinants
112(11)
5.7 Fermionic Systems with Pfaffians
123(6)
5.8 Energy and Correlation Functions
129(1)
5.9 Practical Implementation
129(2)
6 Optimization of Variational Wave Functions
131(25)
6.1 Introduction
131(1)
6.2 Reweighting Techniques for the Optimization of Wave Functions
132(2)
6.3 Energy Derivatives
134(3)
6.4 The Stochastic Reconfiguration
137(9)
6.5 Stochastic Reconfiguration as a Projection Technique
146(1)
6.6 The Linear Method
147(5)
6.7 Calculations of Derivatives in the Jastrow-Slater Case
152(4)
7 Time-Dependent Variational Monte Carlo
156(9)
7.1 Introduction
156(1)
7.2 Real-Time Evolution of the Variational Parameters
157(4)
7.3 An Example for the Quantum Quench in One Dimension
161(4)
Part IV Projection Techniques
165(68)
8 Green's Function Monte Carlo
167(22)
8.1 Basic Notions and Formal Derivations
167(3)
8.2 Single Walker Technique
170(3)
8.3 Importance Sampling
173(5)
8.4 The Continuous-Time Limit
178(2)
8.5 Many Walkers Formulation
180(8)
8.6 Practical Implementation
188(1)
9 Reptation Quantum Monte Carlo
189(10)
9.1 A Simple Path Integral Technique
189(2)
9.2 A Simple Way to Sample Configurations
191(4)
9.3 The Bounce Algorithm
195(1)
9.4 The Continuous-Time Limit
196(1)
9.5 Practical Implementation
197(2)
10 Fixed-Node Approximation
199(15)
10.1 The Sign Problem
199(5)
10.2 A Simple Example on the Continuum
204(4)
10.3 A Simple Example on the Lattice
208(1)
10.4 The Fixed-Node Approximation on the Lattice
209(4)
10.5 Practical Implementation
213(1)
11 Auxiliary Field Quantum Monte Carlo
214(19)
11.1 Introduction
214(2)
11.2 Trotter Approximation
216(1)
11.3 Hubbard-Stratonovich Transformation
217(2)
11.4 The Path-Integral Representation
219(4)
11.5 Sequential Updates
223(5)
11.6 Ground-State Energy and Correlation Functions
228(1)
11.7 Simple Cases without Sign Problem
228(3)
11.8 Practical Implementation
231(2)
Part V Advanced Topics
233(28)
12 Realistic Simulations on the Continuum
235(26)
12.1 Introduction and Motivations
235(2)
12.2 Variational Wave Function with Localized Orbitals
237(7)
12.3 Size Consistency of the Variational Wave Functions
244(1)
12.4 Optimization of the Variational Wave Functions
245(7)
12.5 Lattice-Regularized Diffusion Monte Carlo
252(4)
12.6 An Improved Scheme for the Lattice Regularization
256(5)
Appendix Pseudo-Random Numbers Generated by Computers 261(3)
References 264(8)
Index 272
Federico Becca is a researcher at the National Research Council (CNR) working in the theoretical group of the Condensed Matter section of the International School for Advanced Studies (SISSA) in Trieste. His research focuses on different aspects of correlated systems on the lattice. His major scientific contributions include advances in frustrated magnets, superconductivity from strong electronic correlation, disordered fermionic and bosonic models, and Mott metal-insulator transitions. Sandro Sorella is Professor of Condensed Matter Physics at the International School of Advanced Studies (SISSA) in Trieste. His focus is on the study of strongly-correlated electron systems by advanced numerical simulation techniques based on quantum Monte Carlo. He has developed novel Monte Carlo algorithms that are now widely used and considered state-of-the-art in the field.