Coulomb analogy for nonhermitian degeneracies near quantum phase transitions

TL;DR

This paper introduces a method to analyze degeneracies in complex-extended Hamiltonians, revealing their behavior near quantum phase transitions and drawing parallels with complex zeros of partition functions.

Contribution

It presents a novel approach to measure and classify degeneracies in non-Hermitian systems, linking them to quantum phase transition phenomena.

Findings

Degeneracies behave like complex zeros of a partition function.

The method enables classification of quantum phase transitions based on degeneracy distributions.

Degeneracies are studied on the Riemann sheet of a selected energy level.

Abstract

Degeneracies near the real axis in a complex-extended parameter space of a hermitian Hamiltonian are studied. We present a method to measure distributions of such degeneracies on the Riemann sheet of a selected level and apply it in classification of quantum phase transitions. The degeneracies are shown to behave similarly as complex zeros of a partition function.