Many-body localization in infinite chains

TL;DR

This paper studies the transition between ergodic and many-body localized phases in infinite spin chains, analyzing order decay and entanglement growth to characterize the phase boundary and critical behavior.

Contribution

It provides a detailed analysis of phase transition signatures in infinite chains, highlighting the limitations of small-system exact diagonalizations for phase boundary determination.

Findings

Exponential decay of order parameter in localized phase

Subballistic entanglement growth in ergodic phase

Discrepancies between infinite and small-system analyses

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 $S_{\textrm{ent}}(t)$ 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 $\nu\sim 0.9$. The entanglement entropy in the ergodic phase grows subballistically, $S_{\textrm{ent}}(t)\sim t^\alpha$, $\alpha\leq 1$, with $\alpha$ 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.