Structure of typical states of a disordered Richardson model and many-body localization

Physical Review B - Condensed Matter and Materials Physics

Volumn 84, Issue 9, 2011, Pages

  Buccheri, F ^a,b   De Luca, A ^a,b   Scardicchio, A ^b,c  

^a SISSA   (Italy)

^b SEZIONE DI TRIESTE   (Italy)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80053557710     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.84.094203     Document Type: Article

References (38)

1. D. Basko, I. Aleiner, and B. Altshuler, Ann. Phys. APNYA6 0003-4916 10.1016/j.aop.2005.11.014 321, 1126 (2006). (Pubitemid 43560343)
2. D. Basko, I. Aleiner, and B. Altshuler, e-print arXiv: cond-mat/0602510 (2006).
3. P. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.109.1492 109, 1492 (1958).
4. B. Altshuler, H. Krovi, and J. Roland, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.1002116107 107, 12446 (2010).
5. S. Knysh and V. Smelyanskiy, e-print arXiv: 1005.3011 (2010).
6. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, Science SCIEAS 0036-8075 10.1126/science.1057726 292, 472 (2001).
7. W. G. Brown, L. F. Santos, D. J. Starling, and L. Viola, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.021106 77, 21106 (2008). (Pubitemid 351230746)
8. A. Pal and D. A. Huse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82. 174411 82, 174411 (2010).
9. V. Oganesyan and D. A. Huse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.155111 75, 155111 (2007).
10. M. Žnidarič, T. Prosen, and P. Prelovšek, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.064426 77, 64426 (2008).
11. R. Richardson, Phys. Lett. PHLTAM 0031-9163 10.1016/0031-9163(63)90259-2 3, 277 (1963).
12. R. Richardson and N. Sherman, Nucl. Phys. NUPHA7 0029-5582 10.1016/0029-5582(64)90687-X 52, 221 (1964).
13. J. Dukelsky, S. Pittel, and G. Sierra, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.76.643 76, 643 (2004). (Pubitemid 40176838)
14. A. Faribault, P. Calabrese, and J. Caux, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.3183720 50, 095212 (2009).
15. A. Faribault, P. Calabrese, and J. S. Caux, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.064503 77, 64503 (2008).
16. A. Faribault, O. El Araby, C. Strater, and V. Gritsev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.83.235124 83, 235124 (2011).
17. M. Mezard, G. Parisi, and M. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
18. D. Meyer and N. Wallach, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1497700 43, 4273 (2002).
19. L. Viola and W. Brown, J. Phys. A: Math. Gen. JMAPAQ 1751-8113 10.1088/1751-8113/40/28/S17 40, 8109 (2007).
20. E. Canovi, D. Rossini, R. Fazio, G. Santoro, and A. Silva, e-print arXiv: 1006.1634 (2010).
21. It is known that the analog of this model in 1D, where the hopping g term just connects nearest-neighbor sites on a chain, reduces to noninteracting fermions by the Jordan-Wigner map and hence localizes for arbitrarily small disorders.
22. J. Caux and J. Mossel, J. Stat. Mech. JMAPAQ 1742-5468 10.1088/1742-5468/2011/02/P02023 (2011) P02023.
23. J. Links, H.-Q. Zhou, R. McKenzie, and M. Gould, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/36/19/201 36, R63 (2003).
24. This problem is not so serious for the ground state and first excited states so one can go to much higher values of N without losing accuracy.
25. G. Sierra, J. M. Roman, and J. Dukelsky, Int. J. Mod. Phys. A IMPAEF 0217-751X 10.1142/S0217751X04020531 19, 381 (2004).
26. F. Dominguez, C. Esebbag, and J. Dukelsky, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/39/37/002 39, 10 (2006). (Pubitemid 44321702)
27. G. Szego, Orthogonal Polynomials (American Mathematical Society, Providence, RI, 1939).
28. α). A similar approach has also been investigated in the recent work.
29. The python code is available on the web at [http://www.sissa.it/ statistical/PapersCode/Richardson/].
30. We have looked for a shortcut to evaluate this sum but, to our knowledge, integrability does not help us here.
31. I. Campbell, J. Flesselles, R. Jullien, and R. Botet, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/20/4/001 20, L47 (1987).
32. In the figure we show also a rational function best fit s (g) = 0.403 0.452 + g 0.656 + g, which has, however, an error of 5 % in the asymptotic value s = 0.403 instead of 0.383, the value obtained by averaging on many more realizations and including smaller N in the fit.
33. S. Kotz and S. Nadarajah, Extreme Value Distributions: Theory and Applications (World Scientific, Singapore, 2000).
34. R. Abou-Chacra, D. Thouless, and P. Anderson, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/6/10/009 6, 1734 (1973).
35. M. Suzuki, Physica PHYSAG 0031-8914 10.1016/0031-8914(71)90226-6 50, 277 (1971).
36. P. Mazur, Physica PHYSAG 0031-8914 10.1016/0031-8914(69)90185-2 43, 533 (1969).
37. Notice that for this inequality to hold, the charges have to be orthogonal with respect to the scalar product. In our case orthogonality is achieved in the thermodynamic limit; see Eq. (7).
38. G. Ortiz, R. Somma, J. Dukelsky, and S. Rombouts, Nucl. Phys. B NUPBBO 0550-3213 10.1016/j.nuclphysb.2004.11.008 707, 421 (2005). (Pubitemid 40131275)