A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

TL;DR

This paper investigates the relationship between non-Hermitian critical points and the correlation length in strongly correlated quantum systems, providing evidence that the point where the energy gap closes corresponds to the inverse correlation length.

Contribution

The paper extends previous conjectures by offering additional evidence and theoretical reasoning for the link between non-Hermitian critical points and correlation lengths in quantum systems.

Findings

Confirmed the conjecture for more systems

Linked the non-Hermitian critical point to the inverse correlation length

Analyzed the dispersion relation of elementary excitations

Abstract

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.