Quantum quenches in the transverse field Ising chain: II. Stationary state properties

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2012, Issue 7, 2012, Pages

  Calabrese, Pasquale ^a   Essler, Fabian H L ^b   Fagotti, Maurizio ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

correlation functions; exact results; stationary states

Indexed keywords

EID: 84864403096     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2012/07/P07022     Document Type: Article

References (97)

1. Calabrese P, Essler F H L and Fagotti M 2012 Quantum quench in the transverse field Ising chain: I. Time evolution of order parameter correlators J. Stat. Mech. P07016
2. Greiner M, Mandel O, Hänsch T W and Bloch I 2002 Collapse and revival of the matter wave field of a Bose-Einstein condensate Nature 419 51 (Pubitemid 34987866)
3. Hofferberth S, Lesanovsky I, Fischer B, Schumm T and Schmiedmayer J 2007 Non-equilibrium coherence dynamics in one-dimensional Bose gases Nature 449 324 (Pubitemid 47449551)
4. Trotzky S, Chen Y-A, Flesch A, McCulloch I P, Schollwöck U, Eisert J and Bloch I 2012 Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas Nature Phys. 8 325
5. Cheneau M, Barmettler P, Poletti D, Endres M, Schauss P, Fukuhara T, Gross C, Bloch I, Kollath C and Kuhr S 2012 Light-cone-like spreading of correlations in a quantum many-body system Nature 481 484
6. Gring M, Kuhnert M, Langen T, Kitagawa T, Rauer B, Schreitl M, Mazets I, Smith D A, Demler E and Schmiedmayer J 2011 Relaxation dynamics and pre-thermalization in an isolated quantum system arXiv:1112.0013
7. Kinoshita T, Wenger T and Weiss D S 2006 A quantum Newtons cradle Nature 440 900
8. Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Nonequilibrium dynamics of closed interacting quantum systems Rev. Mod. Phys. 83 863
9. Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of lattice hard-core bosons Phys. Rev. Lett. 98 50405 (Pubitemid 46203541)
10. Rigol M, Dunjko V and Olshanii M 2008 Thermalization and its mechanism for generic isolated quantum systems Nature 452 854 (Pubitemid 351550863)
11. Calabrese P and Cardy J 2006 Time-dependence of correlation functions following a quantum quench Phys. Rev. Lett. 96 136801
12. Calabrese P and Cardy J 2007 Quantum quenches in extended systems J. Stat. Mech. P06008
13. Cazalilla M A 2006 Effect of suddenly turning on the interactions in the Luttinger model Phys. Rev. Lett. 97 156403 (Pubitemid 44570421)
14. Iucci A and Cazalilla M A 2010 Quantum quench dynamics of the sine-Gordon model in some solvable limits New J. Phys. 12 055019
15. Iucci A and Cazalilla M A 2009 Quantum quench dynamics of the Luttinger model Phys. Rev. A 80 063619
16. Manmana S R, Wessel S, Noack R M and Muramatsu A 2007 Strongly correlated fermions after a quantum quench Phys. Rev. Lett. 98 210405 (Pubitemid 47139673)
17. Cramer M, Dawson C M, Eisert J and Osborne T J 2008 Quenching, relaxation, and a central limit theorem for quantum lattice systems Phys. Rev. Lett. 100 030602 (Pubitemid 351161771)
18. Cramer M and Eisert J 2010 A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states New J. Phys. 12 055020
19. Barthel T and Schollwöck U 2008 Dephasing and the steady state in quantum many-particle systems Phys. Rev. Lett. 100 100601 (Pubitemid 351399128)
20. Cramer M, Flesch A, McCulloch I A, Schollwock U and Eisert J 2008 Exploring local quantum many-body relaxation by atoms in optical superlattices Phys. Rev. Lett. 101 063001
21. Flesch A, Cramer M, McCulloch I P, Schollwoeck U and Eisert J 2008 Probing local relaxation of cold atoms in optical superlattices Phys. Rev. A 78 033608
22. Kollar M and Eckstein M 2008 Relaxation of a one-dimensional Mott insulator after an interaction quench Phys. Rev. A 78 013626
23. Sotiriadis S, Calabrese P and Cardy J 2009 Quantum quench from a thermal initial state Europhys. Lett. 87 20002
24. Roux G 2009 Quenches in quantum many-body systems: one-dimensional Bose-Hubbard model reexamined Phys. Rev. A 79 021608
25. Roux G 2010 Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model Phys. Rev. A 81 053604
26. Sotiriadis S, Fioretto D and Mussardo G 2012 Zamolodchikov-Faddeev algebra and quantum quenches in integrable field theories J. Stat. Mech. P02017
27. Fioretto D and Mussardo G 2010 Quantum quenches in integrable field theories New J. Phys. 12 055015
28. Brandino G P, De Luca A, Konik R M and Mussardo G 2012 Quench dynamics in randomly generated extended quantum models Phys. Rev. B 85 214435
29. Kollath C, Laeuchli A and Altman E 2007 Quench dynamics and non-equilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601 (Pubitemid 46693406)
30. Biroli G, Kollath C and Laeuchli A 2010 Effect of rare fluctuations on the thermalization of isolated quantum systems Phys. Rev. Lett. 105 250401
31. Banuls M C, Cirac J I and Hastings M B 2011 Strong and weak thermalization of infinite non-integrable quantum systems Phys. Rev. Lett. 106 050405
32. Gogolin C, Mueller M P and Eisert J 2011 Absence of thermalization in nonintegrable systems Phys. Rev. Lett. 106 040401
33. Faribault A, Calabrese P and Caux J-S 2009 Quantum quenches from integrability: the fermionic pairing model J. Stat. Mech. P03018
34. Faribault A, Calabrese P and Caux J-S 2009 Bethe Ansatz approach to quench dynamics in the Richardson model J. Math. Phys. 50 095212
35. Barmettler P, Punk M, Gritsev V, Demler E and Altman E 2009 Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench Phys. Rev. Lett. 102 130603
36. Barmettler P, Punk M, Gritsev V, Demler E and Altman E 2010 Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium New J. Phys. 12 055017
37. Kennes D M and Meden V 2010 Relaxation dynamics of an exactly solvable electron-phonon model Phys. Rev. B 82 085109
38. Rigol M and Fitzpatrick M 2011 Initial-state dependence of the quench dynamics in integrable quantum systems Phys. Rev. A 84 033640
39. He K and Rigol M 2012 Initial state dependence of the quench dynamics in integrable quantum systems II: thermal state Phys. Rev. A 85 063609
40. Caneva T, Canovi E, Rossini D, Santoro G E and Silva A 2011 Applicability of the generalized Gibbs ensemble after a quench in the quantum Ising chain J. Stat. Mech. P07015
41. Cazalilla M A, Iucci A and Chung M-C 2012 Thermalization and quantum correlations in exactly solvable models Phys. Rev. E 85 011133
42. Rigol M and Srednicki M 2012 Alternatives to eigenstate thermalization Phys. Rev. Lett. 108 110601
43. Zhang J M, Cui F C and Hu J 2012 The generalized Gibbs ensemble as a pseudo-initial state: its predictive power revealed in a second quench Phys. Rev. E 85 041138
44. Santos L F, Polkovnikov A and Rigol M 2011 Entropy of isolated quantum systems after a quench Phys. Rev. Lett. 107 040601
45. Mossel J and Caux J-S 2012 Exact time evolution of space- and time-dependent correlation functions after an interaction quench in the 1D Bose gas New J. Phys. 14 075006
46. Grisins P and Mazets I E 2011 Thermalization in a one-dimensional integrable system Phys. Rev. A 84 053635
47. Caux J-S and Konik R M 2012 Numerical renormalization based on integrable theories: quantum quenches and their corresponding generalized Gibbs ensembles arXiv:1203.0901
48. Mossel J and Caux J-S 2012 Generalized TBA and generalized Gibbs J. Phys. A: Math. Theor. 45 255001
49. Genway S, Ho A F and Lee D K K 2012 Thermalisation of local observables in small Hubbard lattices arXiv:1204.3036
50. Kormos M, Shashi A, Chou Y-Z and Imambekov A 2012 Interaction quenches in the Lieb-Liniger model arXiv:1204.3889
51. Altman E and Auerbach A 2002 Oscillating superfluidity of bosons in optical lattices Phys. Rev. Lett. 89 250404
52. Barankov R A and Levitov L S 2006 Synchronization in the BCS pairing dynamics as a critical phenomenon Phys. Rev. Lett. 96 230403
53. Yuzbashyan E A and Dzero M 2006 Dynamical vanishing of the order parameter in a fermionic condensate Phys. Rev. Lett. 96 230404 (Pubitemid 43901025)
54. Yuzbashyan E A, Tsyplyatyev O and Altshuler B L 2006 Relaxation and persistent oscillations of the order parameter in fermionic condensate Phys. Rev. Lett. 96 097005 (Pubitemid 43374341)
55. Sciolla B and Biroli G 2010 Quantum quenches and off-equilibrium dynamical transition in the infinite dimensional Bose Hubbard model Phys. Rev. Lett. 105 220401
56. Sciolla B and Biroli G 2011 Dynamical transitions and quantum quenches in mean-field models J. Stat. Mech. P11003
57. Eckstein M, Kollar M and Werner P 2009 Phys. Rev. Lett. 103 056403
58. Schirò M and Fabrizio M 2010 Time-dependent mean field theory for quench dynamics in correlated electron systems Phys. Rev. Lett. 105 076401
59. Schirò M and Fabrizio M 2011 Quantum Quenches in the Hubbard model: time dependent mean field theory and the role of quantum fluctuations Phys. Rev. B 83 165105
60. Gambassi A and Calabrese P 2011 Quantum quenches as classical critical films Europhys. Lett. 95 66007
61. Rossini D, Silva A, Mussardo G and Santoro G 2009 Effective thermal dynamics following a quantum quench in a spin chain Phys. Rev. Lett. 102 127204
62. Rossini D, Suzuki S, Mussardo G, Santoro G E and Silva A 2010 Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behaviour Phys. Rev. B 82 144302
63. Canovi E, Rossini D, Fazio R, Santoro G E and Silva A 2011 Quantum quenches, thermalization and many-body localization Phys. Rev. B 83 094431
64. Calabrese P, Essler F H L and Fagotti M 2011 Quantum quench in the transverse field Ising chain Phys. Rev. Lett. 106 227203
65. Barouch E, McCoy B and Dresden M 1970 Statistical mechanics of the XY model. I Phys. Rev. A 2 1075
66. Barouch E and McCoy B 1971 Statistical mechanics of the XY model. II Phys. Rev. A 3 786
67. Barouch E and McCoy B 1971 Statistical mechanics of the XY model. III Phys. Rev. A 3 2137
68. Igloi F and Rieger H 2000 Long-range correlations in the nonequilibrium quantum relaxation of a spin chain Phys. Rev. Lett. 85 3233
69. Igloi F and Rieger H 2011 Quantum relaxation after a quench in systems with boundaries Phys. Rev. Lett. 106 035701
70. Sengupta K, Powell S and Sachdev S 2004 Quench dynamics across quantum critical points Phys. Rev. A 69 053616
71. Fagotti M and Calabrese P 2008 Evolution of entanglement entropy following a quantum quench: analytic results for the XY chain in a transverse magnetic field Phys. Rev. A 78 010306
72. Silva A 2008 Statistics of the work done on a quantum critical system by quenching a control parameter Phys. Rev. Lett. 101 120603
73. Gambassi A and Silva A 2011 Statistics of the work in quantum quenches, universality and the critical Casimir effect arXiv:1106.2671
74. Campos Venuti L and Zanardi P 2010 Unitary equilibrations: probability distribution of the Loschmidt echo Phys. Rev. A 81 022113
75. Campos Venuti L, Jacobson N T, Santra S and Zanardi P 2011 Exact infinite-time statistics of the Loschmidt echo for a quantum quench Phys. Rev. Lett. 107 010403
76. Foini L, Cugliandolo L F and Gambassi A 2011 Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain Phys. Rev. B 84 212404
77. Rieger H and Iglói F 2011 Semiclassical theory for quantum quenches in finite transverse Ising chains Phys. Rev. B 84 165117
78. Schuricht D and Essler F H L 2012 Dynamics in the Ising field theory after a quantum quench J. Stat. Mech. P04017
79. Jaynes E T 1957 Information theory and statistical mechanics Phys. Rev. 106 620
80. Jaynes E T 1957 Information theory and statistical mechanics II Phys. Rev. 108 171
81. Fagotti M and Calabrese P 2010 Entanglement entropy of two disjoint blocks in XY chains J. Stat. Mech. P04016
82. Fagotti M 2012 New insights into the entanglement of disjoint blocks Europhys. Lett. 97 17007
83. Essler F H L and Fagotti M in preparation
84. Cassidy A C, Clark C W and Rigol M 2011 Generalized thermalization in an integrable lattice system Phys. Rev. Lett. 106 140405
85. Vidal G, Latorre J I, Rico E and Kitaev A 2003 Entanglement in quantum critical phenomena Phys. Rev. Lett. 90 227902
86. Latorre J I, Rico E and Vidal G 2004 Ground state entanglement in quantum spin chains Quant. Inf. Comput. 4 048
87. Peschel I and Eisler V 2009 Reduced density matrices and entanglement entropy in free lattice models J. Phys. A: Math. Theor. 42 504003
88. Fisher M E and Hartwig R E 1968 Toeplitz determinants: some applications, theorems, and conjectures Adv. Chem. Phys. 15 333
89. Au-Yang H and McCoy B 1974 Theory of layered Ising models. II. Spin correlation functions parallel to the layering Phys. Rev. B 10 3885
90. Basor E L and Tracy C A 1991 The Fisher-Hartwig conjecture and generalizations Physica A 177 167
91. Forrester P J and Frankel N E 2004 Applications and generalizations of Fisher-Hartwig asymptotics J. Math. Phys. 45 2003 (Pubitemid 38706901)
92. Deift P, Its A and Krasovsky I 2011 Asymptotics of Toeplitz, Hankel, and Toeplitz + Hankel determinants with Fisher-Hartwig singularities Ann. Math. 174 1243
93. Ehrhardt T 2001 A status report on the asymptotic behaviour of Toeplitz determinants with Fisher-Hartwig singularities Operator Theory Adv. Appl. 124 217
94. Boettcher A and Widom H 2006 Szegö via Jacobi Linear Algebr. Appl. 419 656 (Pubitemid 44427848)
95. Lieb E, Schultz T and Mattis D 1961 Two soluble models of an antiferromagnetic chain Ann. Phys., NY 16 407
96. Niemeyer T H 1967 Some exact calculations on a chain of spins 1/2 Physica 36 377
97. Pfeuty P 1970 The one-dimensional Ising model with a transverse field Ann. Phys., NY 57 79