Relaxation dynamics of disordered spin chains: Localization and the Existence of a Stationary State

Physical Review Letters

Volumn 109, Issue 24, 2012, Pages

  Ziraldo, Simone ^a,b   Silva, Alessandro ^c   Santoro, Giuseppe E ^a,b,c  

^a SISSA   (Italy)

^b DEMOCRITOS NATIONAL SIMULATION CENTER   (Italy)

^c ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

INITIAL STATE; LOCALIZATION PROPERTIES; NUMERICAL EXAMPLE; ONE-DIMENSIONAL MODEL; RELAXATION DYNAMICS; SPIN CHAINS; STATIONARY STATE;

HAMILTONIANS; SPIN DYNAMICS;

RELAXATION PROCESSES;

EID: 84870882411     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.247205     Document Type: Article

References (25)

1. J. von Neumann, Z. Phys. 57, 30 (1929). ZEPYAA 1434-6001 10.1007/BF01339852
2. J. von Neumann, Eur. Phys. J. H 35, 201 (2010). EPJHAD 2102-6459 10.1140/epjh/e2010-00008-5
3. I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80, 885 (2008). RMPHAT 0034-6861 10.1103/RevModPhys.80.885
4. M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sende, and U. Sen, Adv. Phys. 56, 243 (2007). ADPHAH 0001-8732 10.1080/00018730701223200
5. M. Cramer, A. Flesch, I.P. McCulloch, U. Schollwock, and J. Eisert, Phys. Rev. Lett. 101, 063001 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.063001
6. M. Cramer and J. Eisert, New J. Phys. 12, 055020 (2010). NJOPFM 1367-2630 10.1088/1367-2630/12/5/055020
7. A. Flesch, M. Cramer, I.P. McCulloch, U. Schollwock, and J. Eisert, Phys. Rev. A 78, 033608 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.033608
8. S. Trotzky, Y.-A. Chen, A. Flesch, I.P. McCulloch, U. Schollwock, J. Eisert, and I. Bloch, Nat. Phys. 8, 325 (2012). NPAHAX 1745-2473 10.1038/nphys2232
9. E.T. Jaynes, Phys. Rev. 108, 171 (1957). PHRVAO 0031-899X 10.1103/PhysRev.108.171
10. M. Rigol, A. Muramatsu, and M. Olshanii, Phys. Rev. A 74, 053616 (2006). PLRAAN 1050-2947 10.1103/PhysRevA.74.053616
11. T. Barthel and U. Schollwöck, Phys. Rev. Lett. 100, 100601 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.100.100601
12. P. Calabrese, F.H.L. Essler, and M. Fagotti, Phys. Rev. Lett. 106, 227203 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.227203
13. M.A. Cazalilla, A. Iucci, and M.-C. Chung, Phys. Rev. E 85, 011133 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.011133
14. M. Rigol, V. Dunjko, and M. Olshanii, Nature (London) 452, 854 (2008). NATUAS 0028-0836 10.1038/nature06838
15. D.M. Gangardt and M. Pustilnik, Phys. Rev. A 77, 041604 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.77.041604
16. T. Caneva, E. Canovi, D. Rossini, G.E. Santoro, and A. Silva, J. Stat. Mech. (2011) P07015. JSMTC6 1742-5468 10.1088/1742-5468/2011/07/ P07015
17. E. Khatami, M. Rigol, A. Relaño, and A.M. Garcia-Garcia, Phys. Rev. E 85, 050102 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.050102
18. E. Lieb, T. Schultz, and D. Mattis, Ann. Phys. (Berlin) 16, 407 (1961). ANPYA2 0003-4916 10.1016/0003-4916(61)90115-4
19. P. Pfeuty, Ann. Phys. (Berlin) 57, 79 (1970). ANPYA2 0003-4916 10.1016/0003-4916(70)90270-8
20. S. Suzuki, D. Rossini, and G.E. Santoro, arXiv:0910.4055.
21. Using a nondegeneracy condition for the gaps, while often reasonable for single-particle energies, is dangerous for many-body energies. This would lead to the incorrect result that fluctuations are always negligibly small, as discussed in P. Reimann, Phys. Rev. Lett. 101, 190403 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.190403
22. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.109.247205 for details on how to deal with spectral degeneracies and on a quench with off-diagonal correlations in the initial state.
23. C. Gramsch and M. Rigol, Phys. Rev. A 86, 053615 (2012). PLRAAN 1050-2947 10.1103/PhysRevA.86.053615
24. H. Aoki, J. Phys. C 16, L205 (1983). JPSOAW 0022-3719 10.1088/0022-3719/16/6/007
25. S. Ziraldo and G.E. Santoro, arXiv:1211.4465.