Transition between dissipatively stabilized helical states

TL;DR

This paper investigates how boundary-driven dissipative processes induce transitions between different helical states in an XXZ spin chain, revealing non-topologically protected steady states and phase transitions characterized by mixed states.

Contribution

It introduces a perturbative approach to analyze dissipative phase transitions between helical states in an XXZ chain, highlighting non-topological stabilization mechanisms.

Findings

Boundary spins are pinned at large dissipation.

Steady states form a rank-2 mixture of helical states at specific anisotropies.

Transition between states involves mixed states of higher rank.

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.