Spectral and Entanglement Transitions from Non-Hermitian Skin Pumping

TL;DR

This paper explores non-Hermitian physics, revealing how skin effects protect real spectra, introduces a new type of criticality with unique entanglement scaling, and extends the concept of phase-space GBZs to inhomogeneous systems, uncovering novel phenomena.

Contribution

It introduces the concept of scaling-induced non-Hermitian exceptional criticality and extends GBZ theory to inhomogeneous systems with phase-space GBZs.

Findings

Skin effect can protect real spectra without crystal symmetry.

Discovery of scaling-induced non-Hermitian exceptional criticality (SIEC).

Introduction of phase-space GBZs for inhomogeneous NHSE systems.

Abstract

Non-Hermitian physics has unveiled unconventional spectral, topological and critical phenomena, challenging traditional band theories. This thesis advances its understanding in three aspects. First, the non-Hermitian skin effect (NHSE) is shown to protect real spectra in some ansatz models, not relying on crystal symmetries. Second, we discover the phenomenon of scaling-induced non-Hermitian exceptional criticality (SIEC), marked by a unconventional negative dip in entanglement entropy scaling, deviating from the well-established logarithmic behavior. A scaling-dependent generalized Brillouin zone (GBZ) is developed to analytically predict this SIEC. Third, we formulate a theoretical framework for phase-space GBZs, extending the concept of the GBZ to position-dependent systems, particularly for those with spatially inhomogeneous NHSE hoppings. Unprecedented phenomena, including GBZ bifurcation which also protects the stability of real spectra, are revealed, introducing new forms of topological robustness governed by phase-space GBZ bifurcations. This thesis also explores the NHSE in Bethe lattices, where the hyperbolic-like lattice geometry gives rise to a hierarchy of loop sizes that leads to new forms of critical NHSE behavior.