A nonequilibrium quantum phase transition in strongly coupled spin chains

Eduardo Mascarenhas,Giacomo Giudice,Vincenzo Savona

doi:10.22331/q-2017-12-20-40

Eduardo Mascarenhas, Giacomo Giudice + Show 1 more

Open Access

https://doi.org/10.22331/q-2017-12-20-40

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Abstract

We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.

Highlights

We study spin transport in a boundary driven XXZ spin chain
Transport through the XXZ spin chain has been investigated in several studies, both from the perspective of linear response [26,27,28,29,30] and from the point of view of quench-induced dynamics [31,32,33,34]
The study of nonequilibrium critical phenomena has been extended to open quantum systems, where the nonequilibrium character is induced by coupling the system to several external reservoirs [35]

Summary

Introduction

We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. These works have highlighted the possibility of both ballistic and diffusive transport of the spin current and characterized the transition between the different regimes. The boundary driven XXZ spin chain in particular has recently been the object of several studies, as it displays distinct nonequilibrium transport behaviour depending on the driving bias and on the coupling anisotropy [38, 39].

Results

Conclusion