Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses

TL;DR

This paper introduces a new spectral topology classification for non-Hermitian systems based on graph topology, revealing emergent singularities and anomalous responses, and provides a framework for phase diagrams in complex models.

Contribution

It presents the first analytic construction of topological phase diagrams considering multiple non-reciprocal couplings in non-Hermitian systems, linking spectral singularities to physical responses.

Findings

Spectral branching singularities characterize topological classes.

Gap-preserving transitions lead to anomalous response kinks.

Framework applies to multi-band, multi-dimensional, and interacting systems.

Abstract

Within the expanding field of non-Hermitian physics, non-Hermitian pumping has emerged as a key phenomenon, epitomized through the skin effect via extensive boundary mode accumulation modifying the conventional Bloch picture. Beyond redefining bulk-boundary correspondences, we show that non-Hermitian pumping induces an unprecedented type of spectral topology: it admits a classification in terms of graph topology, which is distinct from conventional topological classifications of the eigenstate or energy Riemann surface. Each topological class is characterized by a conformally invariant configuration of spectral branching singularities, with gap-preserving transitions giving rise to emergent band geometry and Berry curvature discontinuities physically manifested as anomalous response kinks. By placing all Hermitian and non-Hermitian lattice Hamiltonians on equal footing, our comprehensive framework also enables the first analytic construction of topological phase diagrams in the presence of multiple non-reciprocal coupling scales, as prototypically demonstrated for the extended non-Hermitian Chern and Kitaev models. Based on general algebraic geometry properties of the energy dispersion, our framework can be directly generalized to multiple bands, dimensions, and even interacting systems. Overall, it reveals the conspiracy of band representations, spectral topology, and complex geometry as it unfolds in directly measurable quantities.