Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss

TL;DR

This paper reveals that complex interactions in an open quantum fermionic chain cause a Liouvillian skin effect, leading to localized eigenmodes and unique boundary-dependent dynamics, advancing the understanding of topological phenomena in strongly interacting open systems.

Contribution

It introduces the concept of interaction-induced Liouvillian skin effect and defines a topological invariant to characterize it in a correlated open quantum system.

Findings

Eigenmodes localize at the right edge under open boundary conditions.

The topological invariant accurately captures the skin effect.

Localized eigenmodes lead to particle accumulation at the boundary.

Abstract

Despite recent intensive research on topological aspects of open quantum systems, effects of strong interactions have not been sufficiently explored. In this paper, we demonstrate that complex-valued interactions induce the Liouvillian skin effect by analyzing a one-dimensional correlated model with two-body loss. We show that, in the presence of complex-valued interactions, eigenmodes and eigenvalues of the Liouvillian strongly depend on boundary conditions. Specifically, we find that complex-valued interactions induce localization of eigenmodes of the Liouvillian around the right edge under open boundary conditions. To characterize the Liouvllian skin effect, we define the topological invariant by using the Liouvillian superoperator. Then, we numerically confirm that the topological invariant captures the Liouvillian skin effect. Furthermore, the presence of the localization of eigenmodes results in the unique dynamics observed only under open boundary conditions: particle accumulation at the right edge in transient dynamics. Our result paves the way to realize topological phenomena in open quantum systems induced by strong interactions.