Mixed-State Topology in Non-Hermitian Systems

TL;DR

This paper explores the topological properties of mixed states in non-Hermitian systems using the Uhlmann phase, revealing new topological features distinct from pure states across various dimensions.

Contribution

It introduces the use of the Uhlmann phase and thermal Uhlmann-Chern number to characterize mixed-state topology in non-Hermitian systems, extending analysis to higher dimensions.

Findings

Mixed states exhibit unique topological features via the Uhlmann phase.

Higher-order mixed-state topology confirmed in 3D and 4D non-Hermitian systems.

Distinct topological characteristics compared to pure states.

Abstract

Non-Hermitian (NH) systems, owing to the existence of exceptional point (or ring and surface), exhibit exotic topological features which are inaccessible in Hermitian systems. While current studies on NH topology has primarily focused on pure states at zero temperature, the topological properties of mixed states remain largely unexplored. In this work, we investigate the mixed-state topology in two-dimensional NH systems using the Uhlmann phase and the thermal Uhlmann-Chern number, both structured via the Uhlmann connection at specific temperatures, revealing distinct topological characteristics compared to those of pure states. Furthermore, we extend our analysis to mixed states in three-dimensional Abelian and four-dimensional non-Abelian NH systems, confirming the existence of the higher-order mixed-state topology. Our study establishes a conceptual and practical pathway for exploring topological phenomena in the mixed-state regime of NH physics.