Many-body localization in infinite chains

T. Enss, F. Andraschko, J. Sirker

Published 2016-08-19Version 1

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 sub-ballistically, $S_{\textrm{ent}}(t)\sim t^\alpha$, $\alpha\leq 1$, with $\alpha$ varying continuously as a function of disorder. A comparison of the obtained phase diagram with exact diagonalization (ED) for small systems shows that ED significantly overestimates the extent of the ergodic phase and therefore cannot be used to analyze the properties of the phase transition.