Many-body localization in infinite chains
  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. 
T. Enss, F. Andraschko, J. Sirker
cond-mat.dis-nn cond-mat.quant-gas cond-mat.stat-mech cond-mat.str-el