Many-body localization in infinite chains

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 $S_{\text{ent}}(t)$ during unitary time evolution. Near the phase transition we find that $m_s(t)$ decays exponentially to its asymptotic value $m_s(\infty )\ne 0$ 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, $m_s(\infty )$ shows an exponential sensitivity on disorder with a critical exponent $\nu \sim 0.9$. The entanglement entropy in the ergodic phase grows subballistically, $S_{\text{ent}}(t)\sim t^{\alpha }$, $\alpha \le 1$, 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.

published version

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Cited by in corpus (4)

• Extended nonergodic states in disordered many-body quantum systems
• Current reversals and metastable states in the infinite Bose-Hubbard chain with local particle loss
• Many-body localization of spinless fermions with attractive interactions in one dimension
• Complete many-body localization in the t-J model caused by random magnetic field