Anomalous mechanisms of the loss of observability in non-Hermitian quantum models

TL;DR

This paper investigates unusual quantum phase transitions in non-Hermitian systems with non-tridiagonal Hamiltonians, revealing anomalous degeneracies linked to multiple exceptional points, contrasting with traditional models.

Contribution

It introduces non-Hermitian quantum models with non-tridiagonal Hamiltonians exhibiting higher degeneracies and multiple exceptional points, expanding understanding of phase transition mechanisms.

Findings

Degeneracy multiplicity exceeds one in new models.

Multiple exceptional points can coincide or differ in order.

Contrasts with traditional tridiagonal models.

Abstract

Quantum phase transitions in certain non-Hermitian systems controlled by non-tridiagonal Hamiltonian matrices are found anomalous. In contrast to the known models with tridiagonal-matrix structure in which the geometric multiplicity of the completely degenerate energy eigenvalue appears always equal to one, this multiplicity is found larger than one in the present models. The phenomenon is interpreted as a confluence of several decoupled Kato's exceptional points of equal or different orders.