Quantum Monte Carlo methods: algorithms for lattice models
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2016
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiii, 488 Seiten Diagramme |
| ISBN: | 9781107006423 |
Internformat
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| 100 | 1 | |a Gubernatis, James E. |e Verfasser |0 (DE-588)1103159402 |4 aut | |
| 245 | 1 | 0 | |a Quantum Monte Carlo methods |b algorithms for lattice models |c J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg) |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 2016 | |
| 300 | |a xiii, 488 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Monte Carlo method | |
| 650 | 4 | |a Many-body problem | |
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| 650 | 0 | 7 | |a Quantenphysik |0 (DE-588)4266670-3 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Monte-Carlo-Simulation |0 (DE-588)4240945-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Vielkörperproblem |0 (DE-588)4078900-7 |D s |
| 689 | 0 | 2 | |a Gittermodell |0 (DE-588)4226961-1 |D s |
| 689 | 0 | 3 | |a Quantenphysik |0 (DE-588)4266670-3 |D s |
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Datensatz im Suchindex
| _version_ | 1804176403317391360 |
|---|---|
| adam_text | Contents
Preface page xi
Part I Monte Carlo basics 1
1 Introduction 3
1.1 The Monte Carlo method 3
1.2 Quantum Monte Carlo 5
1.3 Classical Monte Carlo 6
2 Monte Carlo basics 11
2.1 Some probability concepts 11
2.2 Random sampling 15
2.3 Direct sampling methods 17
2.3.1 Discrete distributions 17
2.3.2 Continuous distributions 20
2.4 Markov chain Monte Carlo 23
2.4.1 Markov chains 24
2.4.2 Stochastic matrices 25
2.5 Detailed balance algorithms 28
2.5.1 Metropolis algorithm 28
2.5.2 Generalized Metropolis algorithms 31
2.5.3 Heat-bath algorithm 33
2.6 Rosenbluth’s theorem 35
2.7 Entropy content 38
Exercises 40
3 Data analysis 43
3.1 Equilibrating the sampling 43
3.2 Calculating averages and estimating errors 46
3.3 Correlated measurements and autocorrelation times 49
v
50
52
55
57
59
61
63
66
66
68
69
70
71
73
75
76
80
82
84
84
86
86
87
92
98
103
106
110
111
111
112
114
115
117
119
121
121
Contents
3.4 Blocking analysis
3.5 Data sufficiency
3.6 Error propagation
3.7 Jackknife analysis
3.8 Bootstrap analysis
3.9 Monte Carlo computer program
Exercises
Monte Carlo for classical many-body problems
4.1 Many-body phase space
4.2 Local updates
4.3 Two-step selection
4.4 Cluster updates
4.4.1 Swendsen-Wang algorithm
4.4.2 Graphical representation
4.4.3 Correlation functions and cluster size
4.5 Worm updates
4.6 Closing remarks
Exercises
Quantum Monte Carlo primer
5.1 Classical representation
5.2 Quantum spins
5.2.1 Longitudinal-field Ising model
5.2.2 Transverse-field Ising model
5.2.3 Continuous-time limit
5.2.4 Zero-field XYmodel
5.2.5 Simulation with loops
5.2.6 Simulation with worms
5.2.7 Ergodicity and winding numbers
5.3 Bosons and Fermions
5.3.1 Bosons
5.3.2 Fermions
5.4 Negative-sign problem
5.5 Dynamics
Exercises
Part II Finite temperature
Finite-temperature quantum spin algorithms
6.1 Feynman’s path integral
Contents Vll
6.2 Loop/cluster update 124
6.2.1 General framework 124
6.2.2 Continuous-time loop/cluster update 127
6.2.3 XXZ models 129
6.2.4 Correlation functions 132
6.2.5 Magnetic fields 136
6.2.6 Large spins ( S |) 137
6.3 High-temperature series expansion 140
6.3.1 Stochastic series expansion 140
6.3.2 “Continuous-time” limit 144
6.4 Worm update 145
6.4.1 Freezing problem 146
6.4.2 Directed-loop algorithm 147
6.4.3 Violation of the detailed balance condition 153
6.4.4 Correlation functions 154
6.4.5 XXZ model 156
6.4.6 On-the-fiy vertex generation 161
6.5 Toward zero temperature 164
6.5.1 Extrapolation to zero temperature 166
6.5.2 Quantum phase transitions 168
6.5.3 Finite-size scaling 170
6.6 Applications to Bosonic systems 174
Exercises 179
Determinant method 180
7.1 Theoretical framework 180
7.1.1 Hubbard-Stratonovich transformations 181
7.1.2 Determinantal weights 185
7.1.3 Single-particle Green’s function 188
7.2 Finite temperature algorithm 189
7.2.1 Matrix representation 190
7.2.2 Metropolis sampling 192
7.2.3 The algorithm 194
7.2.4 Measurements 197
7.3 Hirsch-Fye algorithm 198
7.4 Matrix product stabilization 202
7.5 Comments 209
Exercises 211
8 Continuous-time impurity solvers
8.1 Quantum impurity models
214
214
Contents
viii
8.1.1 Chain representation 216
8.1.2 Action formulation 217
8.2 Dynamical mean-field theory 219
8.2.1 Single-site effective model 219
8.2.2 DMFT approximation 221
8.2.3 DMFT self-consistency loop 222
8.2.4 Simulation of strongly correlated materials 223
8.2.5 Cluster extensions 226
8.3 General strategy 228
8.4 Weak-coupling approach 230
8.4.1 Sampling 232
8.4.2 Determinant ratios and fast matrix updates 233
8.4.3 Measurement of the Green’s function 234
8.4.4 Multi-orbital and cluster impurity problems 236
8.5 Strong-coupling approach 237
8.5.1 Sampling 240
8.5.2 Measurement of the Green’s function 240
8.5.3 Generalization - Matrix formalism 244
8.5.4 Generalization - Krylov formalism 247
8.6 Infinite-C limit: Kondo model 249
8.6.1 Weak-coupling approach 249
8.6.2 Strong-coupling approach 252
8.7 Determinant structure and sign problem 254
8.7.1 Combination of diagrams into a determinant 254
8.7.2 Absence of a sign problem 256
8.8 Scaling of the algorithms 258
Exercises 262
Part III Zero temperature 265
9 Variational Monte Carlo 267
9.1 Variational Monte Carlo 267
9.1.1 The variational principle 267
9.1.2 Monte Carlo sampling 270
9.2 Trial states 272
9.2.1 Slater-Jastrow states 273
9.2.2 Gutzwiller projected states 274
9.2.3 Valence bond states 282
9.2.4 Tensor network states 287
9.3 Trial-state optimization 291
9.3.1 Linear method 293
Contents
IX
9.3.2 Newton’s method 296
9.3.3 Connection between linear and Newton methods 298
9.3.4 Energy variance optimization 298
9.3.5 Stabilization 299
9.3.6 Summary of the linear and Newton’s optimization methods 299
Exercises 301
10 Power methods 302
10.1 Deterministic direct and inverse power methods 302
10.2 Monte Carlo power methods 305
10.2.1 Monte Carlo direct power method 306
10.2.2 Monte Carlo inverse power method 310
10.3 Stochastic reconfiguration 314
10.4 Green’s function Monte Carlo methods 320
10.4.1 Linear method 322
10.4.2 Diffusion Monte Carlo 324
10.4.3 Importance sampling 326
10.5 Measurements 327
10.6 Excited states 329
10.6.1 Correlation function Monte Carlo 329
10.6.2 Modified power method 331
10.7 Comments 334
Exercises 337
11 Fermion ground state methods 338
11.1 Sign problem 338
11.2 Fixed-node method 341
11.3 Constrained-path method 345
11.4 Estimators 349
11.4.1 Mixed estimator 349
11.4.2 Forward walking and back propagation 352
11.5 The algorithms 355
11.6 Constrained-phase method 360
Exercises 363
Part IV Other topics 365
12 Analytic continuation 367
12.1 Preliminary comments 367
12.2 Dynamical correlation functions 370
12.3 Bayesian statistical inference 373
X
Contents
12.3.1 Principle of maximum entropy 375
12.3.2 The likelihood function and prior probability 378
12.3.3 The “best” solutions 380
12.4 Analysis details and the Ockham factor 383
12.5 Practical considerations 388
12.6 Comments 395
Exercises 396
13 Parallelization 398
13.1 Parallel architectures 398
13.2 Single-spin update on a shared-memory computer 399
13.3 Single-spin update on a distributed-memory computer 402
13.4 Loop/cluster update and union-find algorithm 403
13.5 Union-find algorithm for shared-memory computers 408
13.6 Union-find algorithm for distributed-memory computers 411
13.7 Back to the future 413
Appendix A Alias method 416
Appendix B Rejection method 418
Appendix C Extended-ensemble methods 420
Appendix D Loop/cluster algorithms: SU(JV) model 425
Appendix E Long-range interactions 428
Appendix F Thouless’s theorem 432
Appendix G Hubbard-Stratonovich transformations 435
Appendix H Multi-electron propagator 441
Appendix I Zero temperature determinant method 445
Appendix J Anderson impurity model: chain representation 449
Appendix K Anderson impurity model: action formulation 451
Appendix L Continuous-time auxiliary-field algorithm 455
Appendix M Continuous-time determinant algorithm 459
Appendix N Correlated sampling 462
Appendix O The Bryan algorithm 464
References 469
Index 484
QUANTUM MONTE CARLO METHODS
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 algo-
rithms 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 mod-
els and their use within dynamical mean-field theory, along with algorithms for ana-
lytically 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.
j. e. gubernatis works at the Los Alamos National Laboratory. He is a
Fellow of the American Physical Society (APS) and served as a Chair of the
APS’ Division of Computational Physics. He represented the United States on the
Commission of Computational Physics of International Union of Pure and Applied
Physics (IUPAP) for nine years and chaired the Commission for three years.
n. kawashim A is a professor at the University of Tokyo. He is a member of the
Society of Cognitive Science and has been a Steering Committee member for the
public use of the supercomputer at the Institute for Solid State Physics (ISSP) for
the last 15 years. He received the Ryogo Kubo Memorial Prize for his contributions
to the development of loop and cluster algorithms in 2002.
p. werner is a professor at the University of Fribourg. In 2010, he received the
IUPAP Young Scientist Prize in computational physics for the development and
implementation of quantum Monte Carlo methods for impurity models.
|
| any_adam_object | 1 |
| author | Gubernatis, James E. Kawashima, Naoki Werner, Philipp 1975- |
| author_GND | (DE-588)1103159402 (DE-588)1103160117 (DE-588)1103161091 |
| author_facet | Gubernatis, James E. Kawashima, Naoki Werner, Philipp 1975- |
| author_role | aut aut aut |
| author_sort | Gubernatis, James E. |
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| ctrlnum | (OCoLC)953088176 (DE-599)BSZ462695301 |
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| dewey-ones | 530 - Physics |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV043653784 |
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| indexdate | 2024-07-10T07:31:38Z |
| institution | BVB |
| isbn | 9781107006423 |
| language | English |
| lccn | 2015026699 |
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| spelling | Gubernatis, James E. Verfasser (DE-588)1103159402 aut Quantum Monte Carlo methods algorithms for lattice models J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg) Cambridge Cambridge University Press 2016 xiii, 488 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Monte Carlo method Many-body problem Gittermodell (DE-588)4226961-1 gnd rswk-swf Quantenphysik (DE-588)4266670-3 gnd rswk-swf Vielkörperproblem (DE-588)4078900-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Vielkörperproblem (DE-588)4078900-7 s Gittermodell (DE-588)4226961-1 s Quantenphysik (DE-588)4266670-3 s DE-604 Kawashima, Naoki Verfasser (DE-588)1103160117 aut Werner, Philipp 1975- Verfasser (DE-588)1103161091 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029067330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029067330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Gubernatis, James E. Kawashima, Naoki Werner, Philipp 1975- Quantum Monte Carlo methods algorithms for lattice models Monte Carlo method Many-body problem Gittermodell (DE-588)4226961-1 gnd Quantenphysik (DE-588)4266670-3 gnd Vielkörperproblem (DE-588)4078900-7 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4226961-1 (DE-588)4266670-3 (DE-588)4078900-7 (DE-588)4240945-7 |
| title | Quantum Monte Carlo methods algorithms for lattice models |
| title_auth | Quantum Monte Carlo methods algorithms for lattice models |
| title_exact_search | Quantum Monte Carlo methods algorithms for lattice models |
| title_full | Quantum Monte Carlo methods algorithms for lattice models J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg) |
| title_fullStr | Quantum Monte Carlo methods algorithms for lattice models J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg) |
| title_full_unstemmed | Quantum Monte Carlo methods algorithms for lattice models J.E. Gubernatis (Los Alamos National Laboratory), N. Kawashima (University of Tokyo), P. Werner (University of Fribourg) |
| title_short | Quantum Monte Carlo methods |
| title_sort | quantum monte carlo methods algorithms for lattice models |
| title_sub | algorithms for lattice models |
| topic | Monte Carlo method Many-body problem Gittermodell (DE-588)4226961-1 gnd Quantenphysik (DE-588)4266670-3 gnd Vielkörperproblem (DE-588)4078900-7 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | Monte Carlo method Many-body problem Gittermodell Quantenphysik Vielkörperproblem Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029067330&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029067330&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gubernatisjamese quantummontecarlomethodsalgorithmsforlatticemodels AT kawashimanaoki quantummontecarlomethodsalgorithmsforlatticemodels AT wernerphilipp quantummontecarlomethodsalgorithmsforlatticemodels |