Abstract
The many-body localization transition is a dynamical quantum phase transition between a localized and an extended phase. We study this transition in the XXZ model with disordered magnetic field and focus on the time evolution following a global quantum quench. While the dynamics of the bipartite entanglement and spin fluctuations are already known to provide insights into the nature of the many-body localized phases, we discuss the relevance of these quantities in the context of the localization transition. In particular, we observe that near the transition the long time limits of both quantities show behavior similar to divergent thermodynamic fluctuations.
Highlights
Many-body localization (MBL) occurs when Anderson localization[1] persists in the presence of interactions
We have studied the effect of disorder on global quench dynamics in a 1D spin chain and found that the asymptotic behavior of different physical quantities show signatures of the many-body localization transition
More importantly the standard deviation of entanglement at large times behaves very similar to thermodynamic fluctuations and shows a peak near the transition
Summary
Many-body localization (MBL) occurs when Anderson localization[1] persists in the presence of interactions. We consider the anti-ferromagnetic spin1/2 XXZ chain and study the time evolution of the entanglement as well as the bipartite fluctuations following a global quench. The Hamiltonian (1) provides a simple model to study the MBL phenomena numerically.[6,7,13,14,20] This model shows a localization transition at ηc ≈ 3.6 at infinite temperature corresponding to eigenstates in the middle of the spectrum.[13,14] It has been argued that MBL systems have a many-body mobility edge,[4] which was first observed numerically in transverse field Ising chain.[5] The mobility edge has been obtained for the XXZ chain in Ref. and spinless fermions in Ref.
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