Quantum dynamics of disordered spin chains with power-law interactions

Abstract

We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying ($1/r^{\alpha }$) interactions. We focus on two spin-$1/2$ Hamiltonians featuring power-law interactions: Heisenberg and XY and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern $I(t)$, growth of entanglement entropy $S(t)$, and growth of quantum Fisher information $F_Q(t).$ For sufficiently rapidly decaying interactions $\alpha >{\alpha }_c$ we find a many-body localized phase, in which $I(t)$ saturates to a non-zero value, entanglement entropy grows as $S(t)\propto t^{1/\alpha }$, and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short range interacting models). The critical power ${\alpha }_c$ is smaller for the XY model than for the Heisenberg model.

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