Absence of True Localization in Many-Body Localized Phases

A characteristic feature of many-body localization (MBL) is a logarithmic growth of the von Neumann entanglement entropy S after a quantum quench. In lattice systems with particle-number conservation, S is the sum of number entropy S_N and configurational entropy S_conf. Especially, in experiments of ultra cold gases using a quantum gas microscope S_N is easily obtained by observing the particle number distribution p(n) of a subsystem. We have recently shown that the logarithmic growth of the entanglement entropy is accompanied by a slow growth of the number entropy, S_N∼lnln t^[1]. This violates the standard scenario of MBL and raises the question whether the observed behavior is transient or continues to hold at strong disorder in the thermodynamic limit. Here we provide an in-depth numerical study of S_N(t) for the disordered Heisenberg chain and find strong evidence that the system is not fully localized even at strong disorder. Calculating the Rényi number entropy S_N^α(t) for α«1—which is sensitive to large number fluctuations occurring with low probability—we demonstrate that p(n) in one half of the system has a small but continuously growing tail.
[1] M. Kiefer-Emmanouilidis et al., Phys. Rev. Lett. 124, 243601 (2020)