Introduction to the statistical physics of integrable many-body systems:
"Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. "
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Cover Inhaltsverzeichnis |
| Summary: | "Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. " |
| Physical Description: | XIX, 504 S. graph. Darst. |
| ISBN: | 9781107030435 |
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| 245 | 1 | 0 | |a Introduction to the statistical physics of integrable many-body systems |c Ladislav Šamaj ; Zoltán Bajnok |
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| adam_text | Titel: Introduction to the statistical physics of integrable many-body systems
Autor: Šamaj, Ladislav
Jahr: 2013
Contents
Preface page xi
PARTI SPINLESS BÖSE AND FERMI GASES 1
1 Particles with nearest-neighbor interactions: Bethe ansatz and
the ground State 5
1.1 General formalism 5
1.2 Point interactions 8
1.3 Bosons with S -potential: Bethe ansatz equations 12
1.4 Bound states for attractive bosons 18
1.5 Repulsive bosons 20
1.6 Particles with finite hard-core interactions 28
Exercises 29
2 Bethe ansatz: Zero-temperature thermodynamics and excitations 33
2.1 Response of the ground State 34
2.2 Zero-temperature thermodynamics 35
2.3 Low-lying excitations 37
Exercises 41
3 Bethe ansatz: Finite-temperature thermodynamics 45
3.1 The concept of holes 45
3.2 Thermodynamic equilibrium 47
Exercises 50
4 Particles with inverse-square interactions 56
4.1 The two-body scattering problem 57
4.2 The ground-state wavefunction of a product form 58
vi Contents
4.3 Excited states for the trigonometric case 62
Exercises 64
PART II QUANTUM INVERSE-SCATTERING METHOD 69
5 QISM: Yang-Baxter equation 73
5.1 Generalized Bethe ansatz 73
5.2 Derivation ofthe Yang-Baxter equation 75
5.3 Lax Operators, monodromy and transfer matrices 80
5.4 Two-state Solutions of the YBE 82
5.5 Braid-group Solution 85
5.6 Quantum groups 88
Exercises 96
6 QISM: Transfer matrix and its diagonalization 98
6.1 Vertex modeis on the square lattice 98
6.2 Connection with quantum modeis on a chain 101
6.3 Diagonalization of the trigonometric transfer matrix 103
Exercises 108
7 QISM: Treatmentof boundary conditions 110
7.1 Formulation of boundary conditions 110
7.2 Boundary conditions and the inhomogeneous transfer matrix 112
7.3 Diagonalization of the inhomogeneous transfer matrix 113
8 Nested Bethe ansatz for spin-| fermions with 8 -interactions 116
8.1 The scattering problem 116
8.2 Nested Bethe equations for spin- j fermions 119
8.3 Ground State and low-lying excitations 120
Exercises 127
9 Thermodynamics of spin-1 fermions with «S-interactions 130
9.1 Repulsive regime c 0 130
9.2 Attractive regime c 0 136
Exercises 137
PART III QUANTUM SPIN CHAINS 141
10 Quantum Ising chain in a transverse field 145
10.1 Jordan-Wigner transformation 146
10.2 Diagonalization of the quadratic form 148
Contents vii
10.3 Ground-state properties and thermodynamics 150
10.4 Thermodynamics of the classical 2D Ising model 151
Exercises 155
11 XXZ Heisenberg chain: Bethe ansatz and the ground State 158
11.1 Symmetries of the Hamiltonian 158
11.2 Schrödinger equation 159
11.3 Coordinate Bethe ansatz 161
11.4 Orbach parämeterization 164
11.5 The ground State 168
11.6 The absolute ground State for A 1 170
Exercises 171
12 XXZ Heisenberg chain: Ground State in the presence of a
magnetic field 175
12.1 Fundamental integral equation for the A-density 176
12.2 Formula for the magnetic field 180
12.3 Ground-state energy near half-filling 183
Exercises 184
13 XXZ Heisenberg chain: Excited states 187
13.1 Strings 187
13.2 Response of the ground State to a perturbation 193
13.3 Low-lying excitations 195
Exercises 196
14 XXX Heisenberg chain: Thermodynamics with strings 199
14.1 Thermodynamic Bethe ansatz 199
14.2 High-temperature expansion 205
14.3 Low-temperature expansion 205
Exercises 209
15 XXZ Heisenberg chain: Thermodynamics without strings 214
15.1 Quantum transfer matrix 214
15.2 Bethe ansatz equations 216
15.3 Nonlinear integral equations for eigenvalues 219
15.4 Representations of the free energy 223
Exercises 226
16 XYZ Heisenberg chain 230
16.1 Diagonalization of the transfer matrix for the eight-Vertex model 230
16.2 Restricted modeis and the p parameter 236
16.3 XYZ chain: Bethe ansatz equations 239
vüi Contents
16.4 XYZ chain: Ground-state energy 241
16.5 XYZ chain: Critical ground-state properties 243
Exercises 245
17 Integrable isotropic chains with arbitrary spin 248
17.1 Construction of the spin-s scattering matrix 248
17.2 Algebraic Bethe ansatz 251
17.3 Thermodynamics with strings 256
17.4 Ground State, low-lying excitations and low-temperature
properties 257
Exercises 260
PART IV STRONGLY CORRELATED ELECTRONS 263
18 Hubbard model 267
18.1 Hamiltonian and its symmetries 267
18.2 Nested Bethe ansatz 270
18.3 Ground-state properties of the repulsive Hubbard model 274
18.4 Ground-state properties of the attractive Hubbard model 285
18.5 Thermodynamics with strings 286
Exercises 291
19 Kondo effect 296
19.1 Hamiltonian of the s-d exchange Kondo model 296
19.2 Electron-impurity and electron-electron scattering
matrices 298
19.3 Inhomogeneous QISM 301
19.4 Ground State 305
19.5 Thermodynamics with strings 312
19.6 TBA for non-interacting electron gas 315
19.7 Thermodynamics of the impurity 317
19.8 Non-degenerate Anderson model 322
Exercises 324
20 Luttinger many-fermion model 333
20.1 The model and its incorrect Solution by Luttinger 334
20.2 Non-interacting spinless fermions 337
20.3 Interacting spinless fermions 347
20.4 Luttinger fermions with spin 358
Exercises 359
Contents ix
21 Integrable BCS superconductors 362
21.1 Mean-field diagonalization of the pairing Hamiltonian 362
21.2 DBCS model and its Solution 365
21.3 Inhomogeneous twisted XXZ model 367
21.4 Quasi-classical limit 368
21.5 Continuum limit of Richardson s equations 371
Exercises 375
PARTV SINE-GORDON MODEL 379
22 Classical sine-Gordon theory 383
22.1 Continuum limit of a mechanical System 383
22.2 Related modeis 385
22.3 Finite-energy Solutions 386
22.4 Scattering Solutions, time shifts 390
22.5 Integrability, conserved charges 394
Exercises 395
23 Conformal quantization 399
23.1 Massless free boson on the cylinder 400
23.2 Massless free boson on the complex plane 402
23.3 Perturbation of the massless free boson: sine-Gordon theory 409
Exercises 413
24 Lagrangian quantization 415
24.1 Semi-classical considerations, phase shifts 415
24.2 Quantization based on the Klein-Gordon theory 417
24.3 Scattering matrix, reduction formulas 422
24.4 Analytic structure of the scattering matrix 425
Exercises 428
25 Bootstrap quantization 430
25.1 Asymptotic states, scattering matrix 430
25.2 S-matrix properties 431
25.3 Solving the simplest modeis by bootstrap 433
25.4 The sine-Gordon 5-matrix 435
Exercises 440
26 UV-IR relation 442
26.1 Ground-state energy density from perturbed CFT 442
26.2 Ground-state energy from TBA 444
Exercises 452
x Contents
27 Exact finite-volume description from XXZ 454
27.1 Excited states from the lattice 455
27.2 Integral equation for the spectrum 457
27.3 Large-volume expansion 459
27.4 Small-volume expansion 461
Exercises 463
28 Two-dimensional Coulomb gas 464
28.1 Basic facts about the 2D Coulomb gas 464
28.2 Renormalized Mayer expansion 467
28.3 Mapping onto the sine-Gordon model 474
28.4 Thermodynamics of the 2D Coulomb gas 477
Exercises 479
Appendix A Spin and spin Operators on a chain 481
A. 1 Spin of a particle 481
A.2 Spin Operators on a chain 483
Appendix B Elliptic functions 486
B.l The Weierstrass functions 487
B.2 The theta functions 489
B.3 The Jacobi elliptic functions 492
References 496
Index 502
|
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| spelling | Šamaj, Ladislav 1959- Verfasser (DE-588)1035673843 aut Introduction to the statistical physics of integrable many-body systems Ladislav Šamaj ; Zoltán Bajnok 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XIX, 504 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier "Including topics not traditionally covered in the literature, such as (1 + 1)- dimensional quantum field theory and classical two-dimensional Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. " Quantentheorie Quantum theory Statistical methods Many-body problem Vielteilchentheorie (DE-588)4331960-9 gnd rswk-swf Vielteilchentheorie (DE-588)4331960-9 s DE-604 Bajnok, Zoltán 1967- Verfasser (DE-588)1035674572 aut http://assets.cambridge.org/97811070/30435/cover/9781107030435.jpg Cover HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026018420&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Šamaj, Ladislav 1959- Bajnok, Zoltán 1967- Introduction to the statistical physics of integrable many-body systems Quantentheorie Quantum theory Statistical methods Many-body problem Vielteilchentheorie (DE-588)4331960-9 gnd |
| subject_GND | (DE-588)4331960-9 |
| title | Introduction to the statistical physics of integrable many-body systems |
| title_auth | Introduction to the statistical physics of integrable many-body systems |
| title_exact_search | Introduction to the statistical physics of integrable many-body systems |
| title_full | Introduction to the statistical physics of integrable many-body systems Ladislav Šamaj ; Zoltán Bajnok |
| title_fullStr | Introduction to the statistical physics of integrable many-body systems Ladislav Šamaj ; Zoltán Bajnok |
| title_full_unstemmed | Introduction to the statistical physics of integrable many-body systems Ladislav Šamaj ; Zoltán Bajnok |
| title_short | Introduction to the statistical physics of integrable many-body systems |
| title_sort | introduction to the statistical physics of integrable many body systems |
| topic | Quantentheorie Quantum theory Statistical methods Many-body problem Vielteilchentheorie (DE-588)4331960-9 gnd |
| topic_facet | Quantentheorie Quantum theory Statistical methods Many-body problem Vielteilchentheorie |
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