Liouvillian Skin Effect in an Exactly Solvable Model

TL;DR

This paper provides an exact solution to a dissipative topological SSH chain, revealing a Liouvillian skin effect that causes boundary-sensitive dynamics, steady state currents, and diverging relaxation times, highlighting the role of topology in open quantum systems.

Contribution

It introduces an exactly solvable model demonstrating the Liouvillian skin effect in a dissipative topological system, connecting non-Hermitian physics with open quantum dynamics.

Findings

Liouvillian skin effect causes boundary-sensitive damping.

Steady state currents observed in finite periodic systems.

Diverging relaxation times in large systems.

Abstract

The interplay between dissipation, topology and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions. Here we exactly solve a quantum mechanical Lindblad master equation describing a dissipative topological Su-Schrieffer-Heeger (SSH) chain of fermions for both open boundary condition (OBC) and periodic boundary condition (PBC). We find that the extreme sensitivity on the boundary conditions associated with the non-Hermitian skin effect is directly reflected in the rapidities governing the time evolution of the density matrix giving rise to a Liouvillian skin effect. This leads to several intriguing phenomena including boundary sensitive damping behavior, steady state currents in finite periodic systems, and diverging relaxation times in the limit of large systems. We illuminate how the role of topology in these systems differs in the effective non-Hermitian Hamiltonian limit and the full master equation framework.