The generalized Gibbs ensemble for Heisenberg spin chains

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2013, Issue 7, 2013, Pages

  Pozsgay, Balázs ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

correlation functions; integrable spin chains (vertex models); quantum integrability (Bethe ansatz); quantum quenches

Indexed keywords

EID: 84881486950     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2013/07/P07003     Document Type: Article

References (57)

1. Rigol M, Dunjko V and Olshanii M 2008 Thermalization and its mechanism for generic isolated quantum systems Nature 452 854 arXiv:0708.1324 [cond-mat.stat-mech] (Pubitemid 351550863)
2. Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Colloquium: nonequilibrium dynamics of closed interacting quantum systems Rev. Mod. Phys. 83 863
3. 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 1D lattice hard-core bosons Phys. Rev. Lett. 98 050405 [arXiv:cond-mat/0604476] (Pubitemid 46203541)
4. Caux J-S and Essler F H L 2013 Time evolution of local observables after quenching to an integrable model Phys. Rev. Lett. 110 257203 arXiv:1301.3806 [cond-mat.stat-mech]
5. 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 arXiv:0911.1927 [cond-mat.quant-gas]
6. Rossini D, Silva A, Mussardo G and Santoro G E 2009 Effective thermal dynamics following a quantum quench in a spin chain Phys. Rev. Lett. 102 127204 arXiv:0810.5508 [cond-mat.stat-mech]
7. 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 nonlocal operators and effective thermal behavior Phys. Rev. B 82 144302 arXiv:1002.2842 [cond-mat.stat-mech]
8. 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 arXiv:1204.3911 [cond-mat.quant-gas]
9. Calabrese P, Essler F H L and Fagotti M 2012 Quantum quenches in the transverse field Ising chain: II. Stationary state properties J. Stat. Mech. P07022 arXiv:1205.2211 [cond-mat.stat-mech]
10. Blass B, Rieger H and Iglói F 2012 Quantum relaxation and finite-size effects in the XY chain in a transverse field after global quenches Europhys. Lett. 99 30004 arXiv:1205.3303 [cond-mat.stat-mech]
11. Essler F H L, Evangelisti S and Fagotti M 2012 Dynamical correlations after a quantum quench Phys. Rev. Lett. 109 247206 arXiv:1208.1961 [cond-mat.stat-mech]
12. 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 arXiv:1105.3176 [cond-mat.stat-mech]
13. Fagotti M and Essler F H L 2013 Reduced density matrix after a quantum quench Phys. Rev. B 87 245107 arXiv:1302.6944 [cond-mat.stat-mech]
14. Calabrese P and Cardy J 2007 Quantum quenches in extended systems J. Stat. Mech. P06008 arXiv:0704.1880 [cond-mat.stat-mech]
15. Cassidy A C, Clark C W and Rigol M 2011 Generalized thermalization in an integrable lattice system Phys. Rev. Lett. 106 140405 arXiv:1008.4794 [cond-mat.stat-mech]
16. Gurarie V 2013 Global large time dynamics and the generalized Gibbs ensemble J. Stat. Mech. P02014 arXiv:1209.3816 [cond-mat.stat-mech]
17. Zhang J M, Cui F C and Hu J 2012 Dynamical predictive power of the generalized Gibbs ensemble revealed in a second quench Phys. Rev. E 85 041138
18. Barthel T and Schollwöck U 2008 Dephasing and the steady state in quantum many-particle systems Phys. Rev. Lett. 100 100601 arXiv:0711.4896 [cond-mat.stat-mech] (Pubitemid 351399128)
19. Kollar M and Eckstein M 2008 Relaxation of a one-dimensional Mott insulator after an interaction quench Phys. Rev. A 78 013626 arXiv:0804.2254 [cond-mat.str-el]
20. Cazalilla M A, Iucci A and Chung M-C 2012 Thermalization and quantum correlations in exactly solvable models Phys. Rev. E 85 011133 arXiv:1106.5206 [cond-mat.stat-mech]
21. Iucci A and Cazalilla M A 2009 Quantum quench dynamics of the Luttinger model Phys. Rev. A 80 063619 arXiv:0903.1205 [cond-mat.str-el]
22. Caux J-S and Konik R M 2012 Numerical renormalization based on integrable theories: quantum quenches and their corresponding generalized Gibbs ensembles Phys. Rev. Lett. 109 175301 arXiv:1203.0901 [cond-mat.quant-gas]
23. Mossel J and Caux J-S 2012 Generalized TBA and generalized Gibbs J. Phys. A: Math. Gen. 45 255001 arXiv:1203.1305 [cond-mat.quant-gas]
24. Yang C N and Yang C P 1969 Thermodynamics of a one-dimensional system of bosons with repulsive delta-function interaction J. Math. Phys. 10 1115
25. Takahashi M 1999 Thermodynamics of One-Dimensional Solvable Models (Cambridge: Cambridge University Press)
26. Fioretto D and Mussardo G 2009 Quantum quenches in integrable field theories New J. Phys. 12 055015 arxiv:0911.3345 [cond-mat.stat-mech]
27. Pozsgay B 2011 Mean values of local operators in highly excited Bethe states J. Stat. Mech. P01011 arXiv:1009.4662 [hep-th]
28. Kormos M, Chou Y-Z and Imambekov A 2011 Exact three-body local correlations for excited states of the 1D Bose gas Phys. Rev. Lett. 107 230405 arXiv:1108.0145 [cond-mat.quant-gas]
29. Davies B and Korepin V E 2011 Higher conservation laws for the quantum non-linear Schroedinger equation arXiv:1109.6604 [math-ph]
30. Grabowski M P and Mathieu P 1994 Quantum integrals of motion for the Heisenberg spin chain Mod. Phys. Lett. A 9 2197 arXiv:hep-th/9403149 [hep-th]
31. Grabowski M and Mathieu P 1995 Structure of the conservation laws in integrable spin chains with short range interactions Ann. Phys. 243 299 arXiv:hep-th/9411045 [hep-th]
32. Klauser A and Caux J-S 2011 Equilibrium thermodynamic properties of interacting two-component bosons in one dimension Phys. Rev. A 84 033604 arXiv:1106.4971 [cond-mat.quant-gas]
33. Klümper A 1993 Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains Z. Phys. B 91 507
34. Klümper A 2004 Integrability of quantum chains: theory and applications to the spin-1/2 XXZ chain Quantum Magnetism (Springer Lecture Notes in Physics vol 645) ed U Schollwöck, J Richter, D J J Farnell and R F Bishop (Berlin: Springer) p 349 [arXiv:cond-mat/0502431]
35. Takahashi M, Shiroishi M and Klümper A 2001 Equivalence of TBA and QTM J. Phys. A: Math. Gen. 34 L187
36. Boos H E, Damerau J, Göhmann F, Klümper A, Suzuki J and Weiße A 2008 Short-distance thermal correlations in the XXZ chain J. Stat. Mech. P08010 arXiv:0806.3953 [cond-mat.str-el]
37. Trippe C, Göhmann F and Klümper A 2010 Short-distance thermal correlations in the massive XXZ chain Eur. Phys. J. B 73 253 arXiv:0908.2232 [cond-mat.str-el]
38. Sato J, Aufgebauer B, Boos H, Göhmann F, Klümper A, Takahashi M and Trippe C 2011 Computation of static Heisenberg-chain correlators: control over length and temperature dependence Phys. Rev. Lett. 106 257201 arXiv:1105.4447
39. Klümper A and Sakai K 2002 The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature J. Phys. A: Math. Gen. 35 2173 [arXiv:cond-mat/0112444] (Pubitemid 37026663)
40. Sakai K and Klümper A 2003 Non-dissipative thermal transport in the massive regimes of the XXZ chain J. Phys. A: Math. Gen. 36 11617 [arXiv:cond-mat/0307227] (Pubitemid 37470020)
41. Zvyagin A A and Klümper A 2003 Quantum phase transitions and thermodynamics of quantum antiferromagnets with next-nearest-neighbor couplings Phys. Rev. B 68 144426
42. Trippe C and Klümper A 2007 Quantum phase transitions and thermodynamics of quantum antiferromagnets with competing interactions Low Temp. Phys. 33 920 arXiv:0709.0229 [cond-mat.str-el]
43. 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 arXiv:0810.4845 [cond-mat.other]
44. Bethe H 1931 Zur theorie der metalle Z. Phys. A 71 205
45. Orbach R 1958 Linear antiferromagnetic chain with anisotropic coupling Phys. Rev. 112 309
46. Walker L R 1959 Antiferromagnetic linear chain Phys. Rev. 116 1089
47. Yang C N and Yang C P 1966 One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a finite system Phys. Rev. 150 321
48. Yang C N 1967 Some exact results for the many-body problem in one dimension with repulsive delta-function interaction Phys. Rev. Lett. 19 1312
49. Baxter R J 1982 Exactly Solved Models in Statistical Mechanics (London: Academic)
50. Lüscher M 1976 Dynamical charges in the quantized renormalized massive Thirring model Nucl. Phys. B 117 475
51. Korepin V, Bogoliubov N and Izergin A 1993 Quantum Inverse Scattering Method and Correlation Functions (Cambridge: Cambridge University Press)
52. Göhmann F, Klümper A and Seel A 2004 Integral representations for correlation functions of the XXZ chain at finite temperature J. Phys. A: Math. Gen. 37 7625 [arXiv:hep-th/0405089] (Pubitemid 39057686)
53. Boos H E, Göhmann F, Klümper A and Suzuki J 2007 Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field J. Phys. A: Math. Theor. 40 10699 [arXiv:0705.2716]
54. Boos H, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2006 Algebraic representation of correlation functions in integrable spin chains Ann. Henri Poincaré 7 1395 [arXiv:hep-th/0601132]
55. Tetelman M G 1982 Lorentz group for two-dimensional integrable lattice systems Sov. Phys. - JETP 55 306
56. Thacker H B 1986 Corner transfer matrices and Lorentz invariance on a lattice Physica D 18 348
57. Vermaseren J A M 2000 New features of FORM arXiv:math-ph/0010025