Correlations at PT-symmetric quantum critical point

TL;DR

This paper investigates a PT-symmetric Fermi gas at the critical point, revealing unique correlation and entanglement properties that challenge traditional notions of universality in quantum criticality.

Contribution

It introduces a detailed analysis of a PT-symmetric Fermi gas at the exceptional point, highlighting novel correlation decay and entanglement behavior in non-hermitian quantum systems.

Findings

Green's function decays with a reduced exponent due to the quantum Zeno effect

Ground state entanglement entropy saturates to a finite value despite gapless excitations

Interactions can induce PT-symmetry breaking or open a gap, affecting criticality

Abstract

We consider a PT-symmetric Fermi gas with an exceptional point, representing the critical point between PT-symmetric and symmetry broken phases. The low energy spectrum remains linear in momentum and is identical to that of a hermitian Fermi gas. The fermionic Green's function decays in a power law fashion for large distances, as expected from gapless excitations, albeit the exponent is reduced from $-1$ due to the quantum Zeno effect. In spite of the gapless nature of the excitations, the ground state entanglement entropy saturates to a finite value, independent of the subsystem size due to the non-hermitian correlation length intrinsic to the system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or opens up a gap and protects PT-symmetry, respectively. Our results challenge the concept of universality in non-hermitian systems, where quantum criticality can be masked due to non-hermiticity.