Static and dynamical Stark many-body localization transition in a linear potential

Abstract

We investigate hard-core bosons filled in a lattice chain in the presence of a weak linear potential. In the single-particle case, we find that the critical point of dynamical Stark localization is different from that of static Stark localization. This suggests an intermediate phase in which the eigenstates are Stark-localized, but the dynamic wave functions are extended after quenching. In the many-body case, by comparing the dynamical critical point with the static critical point, we find a many-body intermediate phase that is analogous to the single-particle intermediate phase. Furthermore, we also study the static transition for the ground state and the dynamical transition for domain-wall states. In the ground state, we find that the localization transition point is at $V\ensuremath{\approx}2(U+W)$ for half-filling ($U$ is the nearest-neighbor interaction strength, $W$ is the half-bandwidth). For the typical domain-wall state $|111\ensuremath{\cdots}000\ensuremath{\rangle}$, its dynamical transition points are at $V\ensuremath{\approx}4(U+W)$ and $V\ensuremath{\approx}4(U\ensuremath{-}W)$. By analyzing the distribution of the occupation, we also offer a phenomenological way to estimate the above transition points.