A non-Hermitian analysis of strongly correlated quantum systems

TL;DR

This paper explores a non-Hermitian extension of strongly correlated quantum systems, proposing a method to determine the correlation length in Hermitian interacting systems through non-Hermitian analysis, supported by exact solutions and numerical data.

Contribution

It introduces a novel approach linking non-Hermitian critical points to correlation lengths in Hermitian systems, validated by models like Hubbard and XXZ.

Findings

Non-Hermitian critical points correspond to inverse correlation lengths.

The conjecture is confirmed using exact solutions and finite-size numerical data.

The approach applies to one-dimensional strongly correlated models.

Abstract

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. It is known that a non-Hermitian critical point is equal to the inverse localization length of a Hermitian non-interacting random electron system. We here conjecture that we can obtain in the same way the correlation length of a Hermitian interacting non-random system. We confirm the conjecture using exact solutions and numerical finite-size data of the Hubbard model and the antiferromagnetic XXZ model in one dimension.