Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain. (English) Zbl 1456.82015
Summary: We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.
MSC:
| 82B05 | Classical equilibrium statistical mechanics (general) |
| 81R12 | Groups and algebras in quantum theory and relations with integrable systems |
References:
| [1] | Greiner M, Mandel O, Hänsch T W and Bloch I 2002 Nature419 51 · doi:10.1038/nature00968 |
| [2] | Kinoshita T, Wenger T and Weiss D S 2006 Nature440 900 · doi:10.1038/nature04693 |
| [3] | Hofferberth S, Lesanovsky I, Fischer B, Schumm T and Schmiedmayer J 2007 Nature449 324 · doi:10.1038/nature06149 |
| [4] | Trotzky S, Chen Y-A, Flesch A, McCulloch I P, Schollwöck U, Eisert J and Bloch I 2012 Nature Phys.8 325 · doi:10.1038/nphys2232 |
| [5] | Cheneau M, Barmettler P, Poletti D, Endres M, Schauss P, Fukuhara T, Gross C, Bloch I, Kollath C and Kuhr S 2012 Nature481 484 · doi:10.1038/nature10748 |
| [6] | Gring M, Kuhnert M, Langen T, Kitagawa T, Rauer B, Schreitl M, Mazets I, Adu Smith D, Demler E and Schmiedmayer J 2012 Science337 1318 · doi:10.1126/science.1224953 |
| [7] | Polkovnikov A, Sengupta K, Silva A and Vengalattore M 2011 Rev. Mod. Phys.83 863 · doi:10.1103/RevModPhys.83.863 |
| [8] | Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Phys. Rev. Lett.98 050405 · doi:10.1103/PhysRevLett.98.050405 |
| [9] | Rigol M, Dunjko V and Olshanii M 2008 Nature452 854 · doi:10.1038/nature06838 |
| [10] | Calabrese P and Cardy J 2007 J. Stat. Mech. P06008 · Zbl 1456.81358 |
| [11] | Iucci A and Cazalilla M A 2009 Phys. Rev. A 80 063619 · doi:10.1103/PhysRevA.80.063619 |
| [12] | Barthel T and Schollwöck U 2008 Phys. Rev. Lett.100 100601 · doi:10.1103/PhysRevLett.100.100601 |
| [13] | Kollar M and Eckstein M 2008 Phys. Rev. A 78 013626 · doi:10.1103/PhysRevA.78.013626 |
| [14] | Manmana S R, Wessel S, Noack R M and Muramatsu A 2009 Phys. Rev. B 79 155104 · doi:10.1103/PhysRevB.79.155104 |
| [15] | Barmettler P, Punk M, Gritsev M, Demler E and Altman E 2009 Phys. Rev. Lett.102 130603 · doi:10.1103/PhysRevLett.102.130603 |
| [16] | Barmettler P, Punk M, Gritsev M, Demler E and Altman E 2010 New J. Phys.12 055017 |
| [17] | Rossini D, Silva A, Mussardo G and Santoro G 2009 Phys. Rev. Lett.102 127204 · doi:10.1103/PhysRevLett.102.127204 |
| [18] | Rossini D, Suzuki S, Mussardo G, Santoro G E and Silva A 2010 Phys. Rev. B 82 144302 · doi:10.1103/PhysRevB.82.144302 |
| [19] | Fioretto D and Mussardo G 2010 New J. Phys.12 055015 · Zbl 1375.81169 |
| [20] | Biroli G, Kollath C and Läuchli A M 2010 Phys. Rev. Lett.105 250401 · doi:10.1103/PhysRevLett.105.250401 |
| [21] | Mossel J and Caux J-S 2010 New J. Phys.12 055028 |
| [22] | Gogolin C, Müller M P and Eisert J 2011 Phys. Rev. Lett.106 040401 · doi:10.1103/PhysRevLett.106.040401 |
| [23] | Calabrese P, Essler F H L and Fagotti M 2011 Phys. Rev. Lett.106 227203 · doi:10.1103/PhysRevLett.106.227203 |
| [24] | Calabrese P, Essler F H L and Fagotti M 2012 J. Stat. Mech. P07016 |
| [25] | Calabrese P, Essler F H L and Fagotti M 2012 J. Stat. Mech. P07022 |
| [26] | Rieger H and Iglói F 2011 Phys. Rev. B 84 165117 · doi:10.1103/PhysRevB.84.165117 |
| [27] | Iglói F and Rieger H 2011 Phys. Rev. Lett.106 035701 · doi:10.1103/PhysRevLett.106.035701 |
| [28] | Schuricht D and Essler F H L 2012 J. Stat. Mech. P04017 |
| [29] | Essler F H L, Evangelisti S and Fagotti M 2012 Phys. Rev. Lett.109 247206 · doi:10.1103/PhysRevLett.109.247206 |
| [30] | Blass B, Rieger H and Iglói F 2012 Europhys. Lett.99 30004 · doi:10.1209/0295-5075/99/30004 |
| [31] | Fagotti M 2013 Phys. Rev. B 87 165106 · doi:10.1103/PhysRevB.87.165106 |
| [32] | Heyl M, Polkovnikov A and Kehrein S 2013 Phys. Rev. Lett.110 135704 · doi:10.1103/PhysRevLett.110.135704 |
| [33] | Rigol M and Fitzpatrick M 2011 Phys. Rev. A 84 033640 · doi:10.1103/PhysRevA.84.033640 |
| [34] | Cazalilla M A, Iucci A and Chung M-C 2012 Phys. Rev. E 85 011133 · doi:10.1103/PhysRevE.85.011133 |
| [35] | Kormos M, Chou Y-Z and Imambekov A 2011 Phys. Rev. Lett.107 230405 · doi:10.1103/PhysRevLett.107.230405 |
| [36] | Pozsgay B 2011 J. Stat. Mech. P01011 · Zbl 1456.82213 |
| [37] | Mossel J and Caux J-S 2012 New J. Phys.14 075006 |
| [38] | Caux J-S and Konik R M 2012 Phys. Rev. Lett.109 175301 · doi:10.1103/PhysRevLett.109.175301 |
| [39] | Foini L, Cugliandolo L F and Gambassi A 2012 J. Stat. Mech. P09011 |
| [40] | Gritsev V, Demler E, Lukin M and Polkovnikov A 2007 Phys. Rev. Lett.99 200404 · doi:10.1103/PhysRevLett.99.200404 |
| [41] | Moeckel M and Kehrein S 2009 Ann. Phys.324 2146 · Zbl 1177.82086 · doi:10.1016/j.aop.2009.03.009 |
| [42] | Pozsgay B 2011 J. Stat. Mech. P01011 · Zbl 1456.82213 |
| [43] | Mitra A and Giamarchi T 2011 Phys. Rev. Lett.107 150602 · doi:10.1103/PhysRevLett.107.150602 |
| [44] | Mitra A 2013 Phys. Rev. B 87 205109 · doi:10.1103/PhysRevB.87.205109 |
| [45] | Karrasch C, Rentrop J, Schuricht D and Meden V 2012 Phys. Rev. Lett.109 126406 · doi:10.1103/PhysRevLett.109.126406 |
| [46] | Cassidy A C, Clark C W and Rigol M 2011 Phys. Rev. Lett.106 140405 · doi:10.1103/PhysRevLett.106.140405 |
| [47] | Gurarie V 2013 J. Stat. Mech. P02014 · Zbl 1456.82588 |
| [48] | Demler E and Tsvelik A M 2012 Phys. Rev. B 86 115448 · doi:10.1103/PhysRevB.86.115448 |
| [49] | Fagotti M and Essler F H L 2013 Phys. Rev. B 87 245107 · doi:10.1103/PhysRevB.87.245107 |
| [50] | Caux J-S and Essler F H L 2013 Phys. Rev. Lett.110 257203 · doi:10.1103/PhysRevLett.110.257203 |
| [51] | Mussardo G 2013 arXiv:1304.7599 |
| [52] | Deutsch J M 1991 Phys. Rev. A 43 2046 · doi:10.1103/PhysRevA.43.2046 |
| [53] | Srednicki M 1994 Phys. Rev. E 50 888 · doi:10.1103/PhysRevE.50.888 |
| [54] | Rigol M, Dunjko V and Olshanii M 2008 Nature452 854 · doi:10.1038/nature06838 |
| [55] | Korepin V E, Izergin A G and Bogoliubov N M 1993 Quantum Inverse Scattering Method, Correlation Functions and Algebraic Bethe Ansatz (Cambridge: Cambridge University Press) · Zbl 0787.47006 · doi:10.1017/CBO9780511628832 |
| [56] | Prosen T 2011 Phys. Rev. Lett.106 217206 · doi:10.1103/PhysRevLett.106.217206 |
| [57] | Pereira R and Sirker J 2012 private communications |
| [58] | Fagotti M, Calabrese P, Collura M and Essler F H L in preparation |
| [59] | Klümper A 1993 Z. Phys. B 91 507 · doi:10.1007/BF01316831 |
| [60] | Destri C and de Vega H J 1995 Nucl. Phys. B 438 314 · Zbl 1052.82529 · doi:10.1016/0550-3213(94)00547-R |
| [61] | Bortz M and Göhmann F 2005 Eur. Phys. J. B 46 399 · doi:10.1140/epjb/e2005-00272-6 |
| [62] | Boos H E, Göhmann F, Klümper A and Suzuki J 2007 J. Phys. A: Math. Theor.40 10699 · Zbl 1147.82316 · doi:10.1088/1751-8113/40/35/001 |
| [63] | Boos H E and Göhmann F 2009 J. Phys. A: Math. Theor.42 315001 · Zbl 1179.82023 · doi:10.1088/1751-8113/42/31/315001 |
| [64] | Trippe C, Göhmann F and Klümper A 2010 Eur. Phys. J. B 73 253 · doi:10.1140/epjb/e2009-00417-7 |
| [65] | Boos H E, Damerau J, Göhmann F, Klümper A, Suzuki J and Weiße A 2008 J. Stat. Mech. P08010 |
| [66] | Muramoto N and Takahashi M 1999 J. Phys. Soc. Japan68 2908 · doi:10.1143/JPSJ.68.2098 |
| [67] | Klümper A and Sakai K 2002 J. Phys. A: Math. Gen.35 2173 · Zbl 1002.82019 · doi:10.1088/0305-4470/35/9/307 |
| [68] | Sakai K and Klümper A 2003 J. Phys. A: Math. Gen.36 11617 · Zbl 1039.82028 · doi:10.1088/0305-4470/36/46/006 |
| [69] | Göhmann F, Klümper A and Seel A 2004 J. Phys. A: Math. Gen.37 7625 · Zbl 1075.82004 · doi:10.1088/0305-4470/37/31/001 |
| [70] | Boos H E, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2006 Ann. Henri Poincare7 1395 · Zbl 1115.82008 · doi:10.1007/s00023-006-0285-5 |
| [71] | Boos H E, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2007 Commun. Math. Phys.272 263 · Zbl 1138.82008 · doi:10.1007/s00220-007-0202-x |
| [72] | Boos H E, Jimbo M, Miwa T, Smirnov F and Takeyama Y 2009 Commun. Math. Phys286 875 · Zbl 1173.82003 · doi:10.1007/s00220-008-0617-z |
| [73] | Jimbo M, Miwa T and Smirnov F 2009 J. Phys. A: Math. Theor.42 304018 · Zbl 1179.82030 · doi:10.1088/1751-8113/42/30/304018 |
| [74] | Pozsgay B 2013 arXiv:1304.5374 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
