Two-parameter Family-Vicsek scaling in a dissipative XXZ spin chain

TL;DR

This paper extends Family-Vicsek scaling to quantum spin chains with dissipation, revealing how magnetization fluctuations grow and saturate under different regimes, bridging classical scaling concepts with quantum dissipative dynamics.

Contribution

It introduces a two-parameter FV scaling framework for dissipative quantum spin chains and derives a closed-form expression in the non-interacting limit, connecting classical and quantum fluctuation behaviors.

Findings

FV roughness exhibits two-parameter scaling in dissipative quantum systems.

Ballistic growth persists in non-interacting chains despite dissipation.

Dissipation dominates the dynamics in interacting chains, leading to collapse of fluctuations.

Abstract

Family-Vicsek (FV) scaling provides an understanding for the growth and finite-size saturation of fluctuations in classical systems. Here, we extend the FV roughness to transferred segment magnetization after quantum quenches in a dissipative XXZ spin chain with homogeneous gain and loss, starting from a nonequilibrium steady state with finite magnetization. In the non-interacting limit, we derive a closed-form expression for the roughness in the presence of dissipation. It displays two-parameter FV scaling and smoothly interpolates between the clean ballistic behavior and the dissipation dominated scalings. For interacting chains, tensor-network simulations show that the non-dissipative ballistic growth at finite magnetization is robust, whereas the full Lindblad evolution is generically controlled by the dissipative relaxation time and exhibits a dissipation-dominated collapse.