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Quantum Mechanics

Dynamics in many-body localized quantum systems without disorder

Profile image of MARKUS MUELLERMARKUS MUELLER

2015, Physical Review B

https://doi.org/10.1103/PHYSREVB.91.184202
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Abstract

We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation invariant Hamiltonian. We show that dynamics starting from a random initial configuration are non-perturbatively slow in the hopping strength, and potentially genuinely non-ergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, that are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and ways how to observe the discussed non-ergodic dynamics.

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References (37)

  1. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
  2. L. Fleishman, D. C. Licciardello and P. W. Anderson, Phys. Rev. Lett. 40, 1340 (1978). L. Fleishman and P. W. Anderson, Phys. Rev. B 21, 2366 (1980).
  3. R. Berkovits and B. I. Shklovskii, J. Phys. Cond. Matter 11, 779 (1999).
  4. D. M. Basko, I. L. Aleiner and B. L. Altshuler, Ann. Phys. 321, 1126 (2006).
  5. I. V. Gornyi, A. D. Mirlin and D. G. Polyakov, Phys. Rev. Lett. 95, 206603 (2005).
  6. V. Oganesyan and D. A. Huse, Phys. Rev. B 75, 155111 (2007).
  7. A. Pal and D. A. Huse, Phys. Rev. B 82, 174411 (2010).
  8. J. Z. Imbrie, arXiv:1403.7837 (2014).
  9. B. Bauer and C. Nayak, J. Stat. Mech. (2013) P09005.
  10. J. A. Kjäll, J. H. Bardarson and F. Pollmann, Phys. Rev. Lett. 113, 107204 (2014).
  11. D. A. Huse, R. Nandkishore and V. Oganesyan, Phys. Rev. B 90, 174202 (2014).
  12. M. Serbyn, Z. Papić and D. A. Abanin, Phys. Rev. Lett. 111, 12 7201 (2013).
  13. V. Ros, M. Müller and A. Scardicchio, Nuclear Physics, Section B (2015), pp. 420-465.
  14. A. Chandran, I. H. Kim, G. Vidal, D. A. Abanin, arXiv:1407.8480 (2014).
  15. Y. Kagan and L. A. Maximov, Sov. Phys. JETP 60, 1 (1984).
  16. G. Carleo, F. Becca, M. Schiró and M. Fabrizio, Scientific Reports 2, 243 (2012).
  17. W. De Roeck and F. Huveneers, Comm. Mat. Phys. 332, 1017 (2014).
  18. W. De Roeck and F. Huveneers, Phys. Rev. B 90, 165137 (2014).
  19. W. De Roeck and F. Huveneers, arXiv:1409.8054, to ap- pear in Proceedings of "Particle systems and PDE's -II" (2014).
  20. M. Schiulaz and M. Müller, AIP Conf. Proc. 1610, 11 (2014).
  21. J. M. Hickey, S. Genway and J. P. Garrahan, arXiv:1405.5780 (2014).
  22. T. Grover and M. P. A. Fisher, J. Stat. Mech. (2014) P10010.
  23. J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan and M. Mézard, Out of equilibrium dynamics in spin-glasses and other glassy systems, in Spin glasses and random fields, A. P. Young Ed., World Scientific (1998).
  24. L. Berthier and G. Biroli, Rev. Mod. Phys. 93, 587 (2011).
  25. G. Biroli, C. Chamon, and F. Zamponi, Phys. Rev. B 78, 224306 (2008).
  26. Z. Nussinov, P. Johnson, M. J. Graf and A. V. Balatsky, arXiv:1209.3823 (2012).
  27. M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, arXiv:1501.05661 (2015).
  28. U. Gavish, Y. Castin, Phys. Rev. Lett. 95, 020401 (2005).
  29. B. Gadway, D. Pertot, R. Reimann, D. Schneble, Phys. Rev. Lett. 105, 045303 (2010).
  30. W. S. Bakr, J. I Gillen, A. Peng, S. Fölling and M. Greiner, Nature 462, 74-77 (2009).
  31. I. Bloch, J. Dalibard and S. Nascimbène, Nature Physics 8, 267-276 (2012).
  32. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
  33. N. Prokof'ev and P. Stamp, Rep. Prog Phys. 63, 669 (2000).
  34. S. Ghosh, R. Parthasarathy, T. F. Rosenbaum, and G. Aeppli, Science 296, 2195 (2002). S. Ghosh, T. F. Rosen- baum, and G. Aeppli, Phys. Rev. Lett. 101, 157205 (2008).
  35. N. Y. Yao, C. R. Laumann, J. I. Cirac, M. D. Lukin, J. E. Moore, arXiv:1410.7407 (2014).
  36. Z. Papić, E. M. Stoudenmire and D. A. Abanin, arXiv:1501.00477 (2015).
  37. J. M. Deutsch, Phys. Rev. A 43, 2046 (1991). M. Sred- nicki, Phys. Rev. E 50, 888 (1994).

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