Hilbert space fragmentation imposed real spectrum of non-Hermitian systems

TL;DR

This paper demonstrates that strong Hilbert space fragmentation, combined with global symmetries, can ensure a real eigenspectrum in non-Hermitian quantum systems, even without $ ext{PT}$ symmetry, and introduces a correlation function to detect exceptional points.

Contribution

It reveals that Hilbert space fragmentation and global symmetries together guarantee real spectra in non-Hermitian systems, a novel insight beyond traditional symmetry considerations.

Findings

Strong HSF and global symmetries lead to real spectra in certain non-Hermitian models.

Analytical proof connecting HSF, symmetries, and real eigenspectra in large interaction limit.

Local correlation functions can detect many-body exceptional points at finite interaction strength.

Abstract

We show that constraints imposed by strong Hilbert space fragmentation (HSF) along with the presence of certain global symmetries can ensure the reality of eigenspectra of non-Hermitian quantum systems; such a reality cannot be guaranteed by global symmetries alone. We demonstrate this insight for two interacting finite chains, namely the fermionic Nelson-Hatano and the Su-Schrieffer-Heeger models, none of which has a $\mathcal{PT}$ symmetry. We show analytically that strong HSF and real spectrum are both consequences of the same dynamical constraints in the limit of large interaction, provided the systems have sufficient global symmetries. We also show that a local equal-time correlation function can detect the many-body exceptional point at a finite critical interaction strength above which the eigenspectrum is real.