Many-body localization in infinite chains

T. Enss; F. Andraschko; J. Sirker

doi:10.1103/PhysRevB.95.045121

paper

Many-body localization in infinite chains

arXiv:1608.05733 · doi:10.1103/PhysRevB.95.045121

Abstract

We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin- $1/2$ Heisenberg chains with binary disorder. Starting from the Néel state, we analyze the decay of antiferromagnetic order $m_{s} (t)$ and the growth of entanglement entropy $S_{ent} (t)$ during unitary time evolution. Near the phase transition we find that $m_{s} (t)$ decays exponentially to its asymptotic value $m_{s} (\infty) \neq = 0$ in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, $m_{s} (\infty)$ shows an exponential sensitivity on disorder with a critical exponent $ν \sim 0.9$ . The entanglement entropy in the ergodic phase grows subballistically, $S_{ent} (t) \sim t^{α}$ , $α \leq 1$ , with $α$ varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.

published version

Many-body localization in infinite chains

Abstract

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