Open-system spin transport and operator weight dissipation in spin chains

We use nonequilibrium steady states to study the effect of dissipation-assisted operator evolution (DAOE) on the scaling behavior of transport in one-dimensional spin chains. We consider three models in the XXZ family: the XXZ model with staggered anisotropy, which is chaotic; XXZ model with no external field and tunable interaction, which is Bethe-ansatz integrable and (in the zero interaction limit) free-fermion integrable; and the disordered XY model, which is free-fermion integrable and Anderson localized. We find evidence that DAOE's effect on transport is controlled by its effect on the system's conserved quantities. To the extent that DAOE preserves those symmetries, it preserves the scaling of the system's transport properties; to the extent it breaks those conserved quantities, it pushes the system towards diffusive scaling of transport.

Automated summary

We use nonequilibrium steady states to study the effect of dissipation-assisted operator evolution (DAOE) on the scaling behavior of transport in one-dimensional spin chains. We consider three models in the XXZ family: the chaotic XXZ model with staggered anisotropy, the Bethe-ansatz integrable XXZ model with no external field and tunable interaction, and the Anderson localized disordered XY model which is free-fermion integrable. Our findings suggest that the effect of DAOE on transport is determined by its impact on the system's conserved quantities, with preservation of the symmetries leading to preserved scaling and breaking of the conserved quantities leading to diffusive scaling of transport.