On truncated generalized Gibbs ensembles in the Ising field theory. (English) Zbl 1457.82064
Summary: We discuss the implementation of two different truncated Generalized Gibbs Ensembles (GGE) describing the stationary state after a mass quench process in the Ising Field Theory. One truncated GGE is based on the semi-local charges of the model, the other on regularized versions of its ultra-local charges. We test the efficiency of the two different ensembles by comparing their predictions for the stationary state values of the single-particle Green’s function \(G(x)=\langle{{\psi}^{\dagger}}(x)\psi (0)\rangle\) of the complex fermion field \(\psi (x)\). We find that both truncated GGEs are able to recover \(G(x)\), but for a given number of charges the semi-local version performs better.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
References:
| [1] | Rigol M, Dunjko V, Yurovsky V and Olshanii M 2007 Phys. Rev. Lett.98 050405 · doi:10.1103/PhysRevLett.98.050405 |
| [2] | Calabrese P and Cardy J 2007 J. Stat. Mech. P06008 · Zbl 1456.81358 · doi:10.1088/1742-5468/2007/06/P06008 |
| [3] | Cramer M, Dawson C M, Eisert J and Osborne T J 2008 Phys. Rev. Lett.100 030602 · doi:10.1103/PhysRevLett.100.030602 |
| [4] | Barthel T and Schollwöck U 2008 Phys. Rev. Lett.100 100601 · doi:10.1103/PhysRevLett.100.100601 |
| [5] | Essler F H L, Evangelisti S and Fagotti M 2012 Phys. Rev. Lett.109 247206 · doi:10.1103/PhysRevLett.109.247206 |
| [6] | Pozsgay B 2013 J. Stat. Mech. P07003 · Zbl 1456.82311 · doi:10.1088/1742-5468/2013/07/P07003 |
| [7] | Fagotti M and Essler F H L 2013 J. Stat. Mech. P07012 https://doi.org/10.1088/1742-5468/2013/07/p07012 · doi:10.1088/1742-5468/2013/07/p07012 |
| [8] | Fagotti M 2014 J. Stat. Mech. P03016 · Zbl 1456.81232 · doi:10.1088/1742-5468/2014/03/P03016 |
| [9] | Fagotti M, Collura M, Essler F H L and Calabrese P 2014 Phys. Rev. B 89 125101 · doi:10.1103/PhysRevB.89.125101 |
| [10] | Wouters B, De Nardis J, Brockmann M, Fioretto D, Rigol M and Caux J-S 2014 Phys. Rev. Lett.113 117202 · doi:10.1103/PhysRevLett.113.117202 |
| [11] | Pozsgay B, Mestyán M, Werner M A, Kormos M, Zaránd G and Takács G 2014 Phys. Rev. Lett.113 117203 · doi:10.1103/PhysRevLett.113.117203 |
| [12] | Sotiriadis S and Calabrese P 2014 J. Stat. Mech. P07024 https://doi.org/10.1088/1742-5468/2014/07/p07024 · doi:10.1088/1742-5468/2014/07/p07024 |
| [13] | Goldstein G and Andrei N 2014 Phys. Rev. A 90 043625 · doi:10.1103/PhysRevA.90.043625 |
| [14] | Brockmann M, Wouters B, Fioretto D, De Nardis J, Vlijm R and Caux J-S 2014 J. Stat. Mech. P12009 · Zbl 1456.82233 · doi:10.1088/1742-5468/2014/12/P12009 |
| [15] | Pozsgay B 2014 J. Stat. Mech. P10045 · Zbl 1456.82312 · doi:10.1088/1742-5468/2014/10/P10045 |
| [16] | Rigol M 2014 Phys. Rev. E 90 031301 · doi:10.1103/PhysRevE.90.031301 |
| [17] | Mestyán M, Pozsgay B, Takács G and Werner M A 2015 J. Stat. Mech. P04001 · Zbl 1456.82298 · doi:10.1088/1742-5468/2015/04/P04001 |
| [18] | Ilievski E, De Nardis J, Wouters B, Caux J-S, Essler F H L and Prosen T 2015 Phys. Rev. Lett.115 157201 · doi:10.1103/PhysRevLett.115.157201 |
| [19] | Eisert J, Friesdorf M and Gogolin C 2015 Nat. Phys.11 124 · doi:10.1038/nphys3215 |
| [20] | Ilievski E, Quinn E, De Nardis J and Brockmann M 2016 J. Stat. Mech. 063101 · Zbl 1456.82050 · doi:10.1088/1742-5468/2016/06/063101 |
| [21] | Piroli L, Vernier E and Calabrese P 2016 Phys. Rev. B 94 054313 · doi:10.1103/PhysRevB.94.054313 |
| [22] | Calabrese P, Essler F H L and Fagotti M 2011 Phys. Rev. Lett.106 227203 · doi:10.1103/PhysRevLett.106.227203 |
| [23] | Calabrese P, Essler F H L and Fagotti M 2012 J. Stat. Mech. P07016 https://doi.org/10.1088/1742-5468/2012/07/p07016 · doi:10.1088/1742-5468/2012/07/p07016 |
| [24] | Calabrese P, Essler F H L and Fagotti M 2012 J. Stat. Mech. P07022 https://doi.org/10.1088/1742-5468/2012/07/p07022 · doi:10.1088/1742-5468/2012/07/p07022 |
| [25] | Fagotti M and Essler F H L 2013 Phys. Rev. B 87 245107 · doi:10.1103/PhysRevB.87.245107 |
| [26] | Caux J-S and Essler F H L 2013 Phys. Rev. Lett.110 257203 · doi:10.1103/PhysRevLett.110.257203 |
| [27] | Essler F H L and Fagotti M 2016 J. Stat. Mech. P064002 https://doi.org/10.1088/1742-5468/2016/06/064002 · Zbl 1456.82585 · doi:10.1088/1742-5468/2016/06/064002 |
| [28] | Calabrese P and Cardy J 2016 J. Stat. Mech. 064003 · Zbl 1456.81359 · doi:10.1088/1742-5468/2016/06/064003 |
| [29] | Cazalilla M A and Chung M-C 2016 J. Stat. Mech. 064004 · Zbl 1456.81051 · doi:10.1088/1742-5468/2016/06/064004 |
| [30] | Calabrese P and Cardy J 2006 Phys. Rev. Lett.96 136801 · doi:10.1103/PhysRevLett.96.136801 |
| [31] | Cazalilla M A 2006 Phys. Rev. Lett.97 156403 · doi:10.1103/PhysRevLett.97.156403 |
| [32] | Gritsev V, Demler E, Lukin M and Polkovnikov A 2007 Phys. Rev. Lett.99 200404 · doi:10.1103/PhysRevLett.99.200404 |
| [33] | Fioretto D and Mussardo G 2010 New J. Phys.12 055015 · Zbl 1375.81169 · doi:10.1088/1367-2630/12/5/055015 |
| [34] | Caux J-S and Konik R M 2012 Phys. Rev. Lett.109 175301 · doi:10.1103/PhysRevLett.109.175301 |
| [35] | Mussardo G 2013 Phys. Rev. Lett.111 100401 · doi:10.1103/PhysRevLett.111.100401 |
| [36] | Kormos M, Collura M and Calabrese P 2014 Phys. Rev. A 89 013609 · doi:10.1103/PhysRevA.89.013609 |
| [37] | Bertini B, Schuricht D and Essler F H L 2014 J. Stat. Mech. P10035 · Zbl 1456.81047 · doi:10.1088/1742-5468/2014/10/P10035 |
| [38] | Collura M, Kormos M and Calabrese P 2014 J. Stat. Mech. P01009 · Zbl 1456.82040 · doi:10.1088/1742-5468/2014/01/P01009 |
| [39] | Sotiriadis S 2016 Phys. Rev. A 94 031605 · doi:10.1103/PhysRevA.94.031605 |
| [40] | Sotiriadis S and Martelloni G 2016 J. Phys. A: Math. Theor.49 095002 · Zbl 1342.82058 · doi:10.1088/1751-8113/49/9/095002 |
| [41] | Cardy J 2016 J. Stat. Mech. 023103 · Zbl 1456.81049 · doi:10.1088/1742-5468/2016/02/023103 |
| [42] | Bertini B, Piroli L and Calabrese P 2016 J. Stat. Mech. 063102 · Zbl 1456.81226 · doi:10.1088/1742-5468/2016/06/063102 |
| [43] | Rakovszky T, Mestyán M, Collura M, Kormos M and Takács G 2016 Nucl. Phys. B 911 805 · Zbl 1346.82021 · doi:10.1016/j.nuclphysb.2016.08.024 |
| [44] | Bastianello A and Sotiriadis S 2016 arXiv:1608.00924 |
| [45] | Gritsev V, Rostunov T and Demler E 2010 J. Stat. Mech. P05012 https://doi.org/10.1088/1742-5468/2010/05/p05012 · doi:10.1088/1742-5468/2010/05/p05012 |
| [46] | Pozsgay B 2011 J. Stat. Mech. P11017 · Zbl 1456.82214 · doi:10.1088/1742-5468/2011/11/P11017 |
| [47] | Panfil M, De J Nardis and Caux J-S 2013 Phys. Rev. Lett.110 125302 · doi:10.1103/PhysRevLett.110.125302 |
| [48] | Collura M, Sotiriadis S and Calabrese P 2013 Phys. Rev. Lett.110 245301 · doi:10.1103/PhysRevLett.110.245301 |
| [49] | Collura M, Sotiriadis S and Calabrese P 2013 J. Stat. Mech. P09025 https://doi.org/10.1088/1742-5468/2013/09/p09025 · doi:10.1088/1742-5468/2013/09/p09025 |
| [50] | Kormos M, Shashi A, Chou Y-Z, Caux J-S and Imambekov A 2013 Phys. Rev. B 88 205131 · doi:10.1103/PhysRevB.88.205131 |
| [51] | De Nardis J, Wouters B, Brockmann M and Caux J-S 2014 Phys. Rev. A 89 033601 · doi:10.1103/PhysRevA.89.033601 |
| [52] | De J Nardis and Caux J-S 2014 J. Stat. Mech. P12012 · Zbl 1456.82043 · doi:10.1088/1742-5468/2014/12/P12012 |
| [53] | Iyer D and Andrei N 2012 Phys. Rev. Lett.109 115304 · doi:10.1103/PhysRevLett.109.115304 |
| [54] | De Nardis J, Piroli L and Caux J-S 2015 Phys. A: Math. Theor.48 43FT01 · Zbl 1330.82041 · doi:10.1088/1751-8113/48/43/43FT01 |
| [55] | Piroli L and Calabrese P 2015 J. Phys. A: Math. Theor.48 454002 · Zbl 1332.82024 · doi:10.1088/1751-8113/48/45/454002 |
| [56] | Piroli L, Calabrese P and Essler F H L 2016 Phys. Rev. Lett.116 070408 · doi:10.1103/PhysRevLett.116.070408 |
| [57] | Piroli L, Calabrese P and Essler F H L 2016 SciPost Phys.1 001 · doi:10.21468/SciPostPhys.1.1.001 |
| [58] | Essler F H L, Mussardo G and Panfil M 2015 Phys. Rev. A 91 051602 · doi:10.1103/PhysRevA.91.051602 |
| [59] | Vernier E and Cubero A C 2016 arXiv:1609.03220 |
| [60] | 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 |
| [61] | Ilievski E, Medenjak M, Prosen T and Zadnik L 2016 J. Stat. Mech. 064008 · Zbl 1456.81238 · doi:10.1088/1742-5468/2016/06/064008 |
| [62] | Ilievski E, Medenjak M and Prosen T 2015 Phys. Rev. Lett.115 120601 · doi:10.1103/PhysRevLett.115.120601 |
| [63] | Doyon B 2004 Correlation functions in integrable quantum field theory PhD Thesis Rutgers University |
| [64] | Iglói F and Rieger H 2000 Phys. Rev. Lett.85 3233 · doi:10.1103/PhysRevLett.85.3233 |
| [65] | Sengupta K, Powell S and Sachdev S 2004 Phys. Rev. A 69 053616 · doi:10.1103/PhysRevA.69.053616 |
| [66] | Fagotti M and Calabrese P 2008 Phys. Rev. A 78 010306 · doi:10.1103/PhysRevA.78.010306 |
| [67] | Rossini D, Silva A, Mussardo G and Santoro G 2009 Phys. Rev. Lett.102 127204 · doi:10.1103/PhysRevLett.102.127204 |
| [68] | Rossini D, Suzuki S, Mussardo G, Santoro G E and Silva A 2010 Phys. Rev. B 82 144302 · doi:10.1103/PhysRevB.82.144302 |
| [69] | Foini L, Cugliandolo L F and Gambassi A 2011 Phys. Rev. B 84 212404 · doi:10.1103/PhysRevB.84.212404 |
| [70] | Rieger H and Iglói F 2011 Phys. Rev. B 84 165117 · doi:10.1103/PhysRevB.84.165117 |
| [71] | Schuricht D and Essler F H L 2012 J. Stat. Mech. P04017 https://doi.org/10.1088/1742-5468/2012/04/p04017 · doi:10.1088/1742-5468/2012/04/p04017 |
| [72] | Foini L, Cugliandolo L F and Gambassi A 2012 J. Stat. Mech. P09011 https://doi.org/10.1088/1742-5468/2012/09/p09011 · doi:10.1088/1742-5468/2012/09/p09011 |
| [73] | Bucciantini L, Kormos M and Calabrese P 2014 J. Phys. A: Math. Theor.47 175002 · Zbl 1291.82067 · doi:10.1088/1751-8113/47/17/175002 |
| [74] | Cassidy A C, Clark C W and Rigol M 2011 Phys. Rev. Lett.106 140405 · doi:10.1103/PhysRevLett.106.140405 |
| [75] | Caux J-S 2016 J. Stat. Mech. 064006 · Zbl 1456.81227 · doi:10.1088/1742-5468/2016/06/064006 |
| [76] | Lieb E H and Liniger W 1963 Phys. Rev.130 1605 · Zbl 0138.23001 · doi:10.1103/PhysRev.130.1605 |
| [77] | Caux J S 2009 J. Math. Phys.50 095214 · Zbl 1248.82017 · doi:10.1063/1.3216474 |
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