Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems

TL;DR

This paper explores the topological properties of dissipative quantum systems using point-gap topology, revealing a complete bulk-boundary correspondence and discovering anomalous skin modes with exponential amplification.

Contribution

It introduces a topological characterization based on the Liouvillian spectrum, establishing a complete bulk-boundary correspondence in dissipative quantum systems, which is rare in physical materials.

Findings

Identification of topologically protected skin modes

Complete bulk-boundary correspondence in dissipative systems

Discovery of anomalous skin modes with exponential amplification

Abstract

The spectral and dynamical properties of dissipative quantum systems, as modeled by a damped oscillator in the Fock space, are investigated from a topological point of view. Unlike a physical lattice system that is naturally under the open boundary condition, the bounded-from-below nature of the Fock space offers a unique setting for understanding and verifying non-Hermitian skin modes under semi-infinity boundary conditions that are elusive in actual physical lattices. A topological characterization based on the complex spectra of the Liouvillian superoperator is proposed and the associated complete set of topologically protected skin modes can be identified, thus reflecting the complete bulk-boundary correspondence of point-gap topology generally absent in realistic materials. Moreover, we discover anomalous skin modes with exponential amplification even though the quantum system is purely dissipative. Our results indicate that current studies of non-Hermitian topological matter can greatly benefit research on quantum open systems and vice versa.