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Dynamical Many-Body Localization in an Integrable Model

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Classical Analogies in the Solution of Quantum Many-Body Problems

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Recently, there has been a lot of interest and progress in understanding Anderson-type localization properties of disordered, interacting many-body systems. Notably, the remarkable phenomenon of many-body localization (MBL) was discovered. In an isolated system, MBL manifests itself in the localization of all eigenstates and leads to the breakdown of ergodicity and violation of the eigenvalue thermalization hypothesis, forcing to revisit the very foundations of quantum statistical mechanics.

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References

  1. D.M. Basko, I.L. Aleiner, B.L. Altshuler, Metal insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. 321(5), 1126–1205 (2006)

    Article  ADS  Google Scholar 

  2. V. Oganesyan, D.A. Huse, Localization of interacting fermions at high temperature. Phys. Rev. B 75(15), 155111 (2007)

    Google Scholar 

  3. A. Pal, D.A. Huse, Many-body localization phase transition. Phys. Rev. B 82(17), 174411 (2010)

    Google Scholar 

  4. J.H. Bardarson, F. Pollmann, J.E. Moore, Unbounded growth of entanglement in models of many-body localization. Phys. Rev. Lett. 109, 017202 (2012)

    Article  ADS  Google Scholar 

  5. S. Iyer, V. Oganesyan, G. Refael, D.A. Huse, Many-body localization in a quasiperiodic system. Phys. Rev. B 87, 134202 (2013)

    Article  ADS  Google Scholar 

  6. B. Bauer, C. Nayak, Area laws in a many-body localized state and its implications for topological order. J. Stat. Mech: Theory Exp. 2013(09), P09005 (2013)

    Article  MathSciNet  Google Scholar 

  7. B. Bauer, C. Nayak, Analyzing many-body localization with a quantum computer. Phys. Rev. X 4(4), 041021 (2014)

    Google Scholar 

  8. J.Z. Imbrie, On many-body localization for quantum spin chains. J. Stat. Phys. 163(5), 998–1048 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Srednicki, Chaos and quantum thermalization. Phys. Rev. E 50, 888–901 (1994)

    Article  ADS  Google Scholar 

  10. J.M. Deutsch, Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046–2049 (1991)

    Article  ADS  Google Scholar 

  11. E. Altman, R. Vosk, Universal dynamics and renormalization in many-body-localized systems. Ann. Rev. Condens. Matter Phys. 6(1), 383–409 (2015)

    Article  ADS  Google Scholar 

  12. D. Huse, R. Nandkishore, Many-body localization and thermalization in quantum statistical mechanics. Ann. Rev. Condens. Matter Phys. 6(1), 15–38 (2015)

    Article  ADS  Google Scholar 

  13. S. Fishman, D.R. Grempel, R.E. Prange, Chaos, quantum recurrences, and Anderson localization. Phys. Rev. Lett. 49, 509–512 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  14. A. Altland, M.R. Zirnbauer, Field theory of the quantum kicked rotor. Phys. Rev. Lett. 77(22), 4536 (1996)

    Article  ADS  Google Scholar 

  15. R.E. Prange, D.R. Grempel, S. Fishman, Solvable model of quantum motion in an incommensurate potential. Phys. Rev. B 29, 6500–6512 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  16. D.R. Grempel, S. Fishman, R.E. Prange, Localization in an incommensurate potential: an exactly solvable model. Phys. Rev. Lett. 49, 833–836 (1982)

    Article  ADS  Google Scholar 

  17. M.V. Berry, Incommensurability in an exactly-soluble quantal and classical model for a kicked rotator. Phys. D: Nonlinear Phenom. 10(3), 369–378 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  18. S. Fishman, D.R. Grempel, R.E. Prange, Localization in a d-dimensional incommensurate structure. Phys. Rev. B 29(8), 4272 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  19. B. Simon, Almost periodic Schrödinger operators iv. The Maryland model. Ann. Phys. 159(1), 157–183 (1985)

    Article  Google Scholar 

  20. G.I. Watson, Spectrum and bandwidth of an exactly soluble incommensurate model. J. Phys. A Math. Gen. 25(2), 345 (1992)

    Article  ADS  Google Scholar 

  21. A. Lazarides, A. Das, R. Moessner, Fate of many-body localization under periodic driving. Phys. Rev. Lett. 115, 030402 (2015)

    Article  ADS  Google Scholar 

  22. P. Ponte, Z. Papić, F. Huveneers, D.A. Abanin, Many-body localization in periodically driven systems. Phys. Rev. Lett. 114, 140401 (2015)

    Article  ADS  Google Scholar 

  23. D.A. Abanin, W. De Roeck, F. Huveneers, Theory of many-body localization in periodically driven systems. Ann. Phys. 372, 1–11 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. P. Ponte, A. Chandran, Z. Papić, D.A. Abanin, Periodically driven ergodic and many-body localized quantum systems. Ann. Phys. 353, 196–204 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  25. L. D’Alessio, A. Polkovnikov, Many-body energy localization transition in periodically driven systems. Ann. Phys. 333, 19–33 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Modak, S. Mukerjee, E.A. Yuzbashyan, B.S. Shastry, Integrals of motion for one-dimensional Anderson localized systems. New J. Phys. 18(3), 033010 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  27. A. Chandran, I.H. Kim, G. Vidal, D.A. Abanin, Constructing local integrals of motion in the many-body localized phase. Phys. Rev. B 91, 085425 (2015)

    Article  ADS  Google Scholar 

  28. M. Serbyn, Z. Papić, D.A. Abanin, Local conservation laws and the structure of the many-body localized states. Phys. Rev. Lett. 111, 127201 (2013)

    Article  ADS  Google Scholar 

  29. R. Modak, S. Mukerjee, E.A. Yuzbashyan, B.S. Shastry, Integrals of motion for one-dimensional Anderson localized systems. New J. Phys. 18(3), 033010 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  30. R.E. Prange, D.R. Grempel, S. Fishman, Wave functions at a mobility edge: an example of a singular continuous spectrum. Phys. Rev. B 28, 7370(R) (1983)

    Article  ADS  Google Scholar 

  31. A.C. Keser, S. Ganeshan, G. Refael, V. Galitski, Dynamical many-body localization in an integrable model. Phys. Rev. B 94, 085120 (2016)

    Article  ADS  Google Scholar 

  32. E.B. Rozenbaum, V. Galitski, Dynamical localization of coupled relativistic kicked rotors. Phys. Rev. B 95, 064303 (2017)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Physics, UNSW Australia, Sydney, NSW, Australia

    Aydın Cem Keser

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  1. Aydın Cem Keser
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Keser, A.C. (2018). Dynamical Many-Body Localization in an Integrable Model. In: Classical Analogies in the Solution of Quantum Many-Body Problems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-00488-0_4

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