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.