Unlimited growth of particle fluctuations 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 . We have recently shown that the logarithmic growth of the entanglement entropy is accompanied by a slow, seemingly unlimited growth of the number entropy, S_N ∼lnln t [1]. This violates the standard scenario of MBL, represented by the l-bit Hamiltonian, 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 never 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 the particle number distribution p(n) in one half of the system has a small but continuously growing tail [2].

[1] M. Kiefer-Emmanouilidis et al., Phys. Rev. Lett. 124, 243601 (2020)

[2] M. Kiefer-Emmanouilidis et al., Phys. Rev. B. 103, 024203 (2021)