57 research outputs found
Out-of-time-order correlations in many-body localized and thermal phases
We use the out-of-time-order (OTO) correlators to study the slow dynamics in
the many-body localized (MBL) phase. We investigate OTO correlators in the
effective ("l-bit") model of the MBL phase, and show that their amplitudes
after disorder averaging approach their long-time limits as power-laws of time.
This power-law dynamics is due to dephasing caused by interactions between the
localized operators that fall off exponentially with distance. The long-time
limits of the OTO correlators are determined by the overlaps of the local
operators with the conserved l-bits. We demonstrate numerically our results in
the effective model and three other more "realistic" spin chain models.
Furthermore, we extend our calculations to the thermal phase and find that for
a time-independent Hamiltonian, the OTO correlators also appear to vanish as a
power law at long time, perhaps due to coupling to conserved densities. In
contrast, we find that in the thermal phase of a Floquet spin model with no
conserved densities the OTO correlator decays exponentially at long times.Comment: 24 pages, 12 figure
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