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On many body localization in random and quasiperiodic potentials
December 15, 2021 @ 10:45 - 11:10 CET
A.S. Aramthottil,1 T. Chanda,1,2 P. Sierant,2,3 J. Zakrzewski1
1Institute of Theoretical Physics, Jagiellonian University in Kraków, Łojasiewicza 11, 30-348 Kraków, Poland
2The Abdus Salam International Center for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
3ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
Our recent numerical results on many-body localization in disordered and quasiperiodic spin chains will be presented. The time dynamics in 1D disordered Heisenberg spin-1/2 chain is studied focusing on a regime of large system sizes and a long time evolution. Performing extensive numerical simulations of the imbalance, a quantity often employed in the experimental studies of MBL, we show that the regime of a slow power-law decay of imbalance persists to disorder strengths exceeding by at least a factor of 2 the current estimates of the critical disorder strength for MBL. Even though we investigate time evolution up to few thousands tunneling times, we observe no signs of the saturation of imbalance that would suggest freezing of system dynamics and provide a smoking gun evidence of MBL. We demonstrate that the situation is qualitatively different when the disorder is replaced by a quasiperiodic potential. In this case, we observe an emergence of a pattern of oscillations of the imbalance that is stable with respect to changes in the system size. This suggests that the dynamics of quasiperiodic systems remain fully local at the longest time scales we reach provided that the quasiperiodic potential is sufficiently strong. The results for time dynamics are further confirmed by a finite-size scaling analysis of eigenstates and spectral statistics across the many-body localization in quasiperiodic systems. The analysis shows the many-body localization transition in quasiperiodic systems belongs to the Berezinskii-Kosterlitz-Thouless class, the same as in the case of uniformly disordered systems. However, the finite size effects are less severe in quasiperiodic systems than in chains with random disorder. Also interestingly, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of onsite magnetizations. Our studies identifies challenges in an unequivocal experimental observation of the phenomenon of MBL [1,2].
The numerical calculations have been possible thanks to PL-Grid Infrastructure. The research has been supported by National Science Centre (Poland) under project 2019/35/B/ST2/00034 (A.S.A., J.Z.). The work of T.C. was realised within the QuantERA grant QTFLAG, financed by National Science Centre (Poland) via grant 2017/25/Z/ST2/03029. We acknowledge the support of Foundation for Polish Science (FNP) through scholarship START (P.S.) as well as via first Polish-French Maria Skłodowska – Pierre Curie award received by D. Delande and J. Zakrzewski.
- P.Sierant, J. Zakrzewski, arXiv:2109.13608
- A.S. Aramsthottil, T. Chanda, P:. Sierant, J. Zakrzewski, arxiv:2109.08408, Phys. Rev. B in press.
