Symmetry-Resolved Entanglement Dynamics in Disordered Bose-Hubbard Chain

Many-body localization (MBL) features long-time persistence of charge-density-like waves (CDWs) of local observables. Is it practical to commence from a modulated state pattern also for nonlocal quantum entanglement? Will such entanglement analogs of CDWs survive still in MBL? From a constituent viewpoint, a great deal of MBL is learnt from 1D spin or fermion systems where carriers are scatter particles. What about the situation when multiple interacting particles cluster in a random-potential background? To tackle these questions, we study symmetry-resolved entanglement entropy in disordered Bose-Hubbard (dBH) chain using numerical quantum quench dynamics. We concentrate on 2 types of inhomogeneous initial states after mapping out the energy-resolved dynamical phase diagram of the model. From time-evolving a line-shape initial product state, we find the sudden formation of robust entropy imbalance across different symmetry sectors, termed entanglement-channel wave (ECW). Intriguingly, ECW melts in MBL under strong-disorder limit. It is tempting to conjecture that melting of ECW and freezing of CDW are duo traits inherent to disorder-induced MBL. Further, by exploiting dynamical consequences of loading bosons onto one site, we find the possibility to realize an interaction-facilitated cluster localization unique to BH-type models at weak disorders. Together, the unraveled rich entanglement dynamics manifests the intrinsic complexity of dBH model from a jointly energy- and symmetry-resolved perspective

Many-body localization transition in the disordered Bose-Hubbard chain

Many-body localization (MBL) of a disordered interacting boson system in one dimension is studied numerically at the filling faction one-half, in terms of level statistics, local compressibility, correlation function, and entanglement entropies. The von Neumann entanglement entropy is decomposed into a particle number entropy and a configuration entropy. The localization lengths are extracted from the two-body correlation function for the many-body-localized states and the corresponding time-evolved states as well. Since the eigenstate configuration entropy nears zero in the localized phase, the localization transition is dominated by the particle number entropy and its fluctuations, as shown by the finite-size analyses of the total entropy and the deviation of the particle number entropy from the ideal thermalization distribution. A dynamical phase diagram is established, consisting of an ergodic thermalized region and a many-body-localized region in a parameter space of the disorder strength and the energy density. These regions are separated by a many-body mobility edge deducible from both the extracted localization length and the entanglement entropy, which also appears consistent with that based on the level-spacing ratio. Starting from 2 particular inhomogeneous initial states, the slow quantum quench dynamics reveals the existence of 3 different localization regions. Their dynamical properties, including the growth behavior, the steady-state entropy scaling, and the emergent channel reflection symmetry, are systematically summarized and compared with the noninteracting Anderson localization. Within this scheme, the recent experimental observation [A. Lukin et al., Science 364, 256 (2019)] might be interpreted as corresponding to the scatter MBL of the trio

Half Metallic Bilayer Graphene

Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers have same magnitude with opposite directions. We propose that lightly charged bilayer graphene in an electric field perpendicular to the graphene plane may be a half metal as a consequence of the inversion and particle-hole symmetry broken in the LAF state. We show this explicitly by using a mean field theory on a 2-layer Hubbard model for the bilayer graphene.Comment: 4+ pages, 4 figure