Abstract
We analyze a $XXZ$ spin-1/2 chain which is driven dissipatively at its boundaries. The dissipative driving is modelled by Lindblad jump operators which only act on both boundary spins. In the limit of large dissipation, we find that the boundary spins are pinned to a certain value and at special values of the interaction anisotropy, the steady states are formed by a rank-2 mixture of helical states with opposite winding numbers. Contrarily to previous stabilization of topological states, these helical states are not protected by a gap in the spectrum of the Lindbladian. By changing the anisotropy, the transition between these steady states takes place via mixed states of higher rank. In particular, crossing the value of zero anisotropy a totally mixed state is found as the steady state. The transition between the different winding numbers via mixed states can be seen in the light of the transitions between different topological states in dissipatively driven systems. The results are obtained developing a perturbation theory in the inverse dissipative coupling strength and using the numerical exact diagonalization and matrix product state methods.
Highlights
Over decades, dissipation has been considered as a destructive influence which destroys the coherence properties of quantum systems
In the limit of large dissipation, we find that the boundary spins are pinned to a certain value and at special values of the interaction anisotropy, the steady states are formed by a rank-2 mixture of helical states with opposite winding numbers
Previous work has uncovered far-from-equilibrium steady states of a helical nature with remarkable transport properties [17,18,19,20]. In this Rapid Communication we focus on a specific configuration of this system for which the jump operators at the boundary sites are identical and lead to an additional reflection symmetry
Summary
Simon Essink ,1 Stefan Wolff, Gunter M. In the limit of large dissipation, we find that the boundary spins are pinned to a certain value and at special values of the interaction anisotropy, the steady states are formed by a rank-2 mixture of helical states with opposite winding numbers. Dissipation has been considered as a destructive influence which destroys the coherence properties of quantum systems This point of view has been revised, since tailored environments have been employed in order to dissipatively drive a quantum many-body system into a desired steady state, the so-called attractor state [1]. Previous work has uncovered far-from-equilibrium steady states of a helical nature with remarkable transport properties [17,18,19,20] In this Rapid Communication we focus on a specific configuration of this system for which the jump operators at the boundary sites are identical and lead to an additional reflection symmetry. As one varies the interaction strength a transition between two helical states occurs, which takes
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