Exceptional Bound States and negative Entanglement Entropy

TL;DR

This paper introduces Exceptional Boundary (EB) states in non-Hermitian systems, characterized by eigenstate coalescence at exceptional points, leading to unique properties like negative entanglement entropy and robustness beyond topological protection.

Contribution

It presents a novel class of EB states arising from geometric defectiveness at exceptional points, distinct from topological or skin boundary states, with unique entanglement properties.

Findings

EB states exhibit negative and anomalously large occupation probabilities.

EB states are robust under various quantum quenches.

Entanglement entropy scaling coefficient can be tuned via perturbations.

Abstract

This work introduces a new class of robust states known as Exceptional Boundary (EB) states, which are distinct from the well-known topological and non-Hermitian skin boundary states. EB states occur in the presence of exceptional points, which are non-Hermitian critical points where eigenstates coalesce and fail to span the Hilbert space. This eigenspace defectiveness not only limits the accessibility of state information, but also interplays with long-range order to give rise to singular propagators only possible in non-Hermitian settings. Their resultant EB eigenstates are characterized by robust anomalously large or negative occupation probabilities, unlike ordinary Fermi sea states whose probabilities lie between zero and one. EB states remain robust after a variety of quantum quenches and give rise to enigmatic negative entanglement entropy contributions. Through suitable perturbations, the coefficient of the logarithmic entanglement entropy scaling can be continuously tuned. EB states represent a new avenue for robustness arising from geometric defectiveness, independent of topological protection or non-reciprocal pumping.