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arXiv:1608.05733 · Physical review. B./Physical review. B

Many-body localization in infinite chains

Tilman Enss, F. Andraschko, Jesko Sirker

Published Jan 17, 2017• 90 citations
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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 N\'eel state, we analyze the decay of antiferromagnetic order ${m}_{s}(t)$ and the growth of entanglement entropy ${S}_{\mathrm{ent}}(t)$ during unitary time evolution. Near the phase transition we find that ${m}_{s}(t)$ decays exponentially to its asymptotic value ${m}_{s}(\ensuremath{\infty})\ensuremath{\ne}0$ 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, ${m}_{s}(\ensuremath{\infty})$ shows an exponential sensitivity on disorder with a critical exponent $\ensuremath{\nu}\ensuremath{\sim}0.9$. The entanglement entropy in the ergodic phase grows subballistically, ${S}_{\mathrm{ent}}(t)\ensuremath{\sim}{t}^{\ensuremath{\alpha}}$, $\ensuremath{\alpha}\ensuremath{\le}1$, with $\ensuremath{\alpha}$ 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.

DOI
10.1103/physrevb.95.045121

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