Correlations at PT-Symmetric Quantum Critical Point

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, although 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.

Automated summary

This study considers a PT-symmetric Fermi gas with an exceptional point, which represents the critical point between PT-symmetric and symmetry broken phases. The results show that despite the presence of gapless excitations, the low energy spectrum of fermions remains linear in momentum and the decay of the Green's function obeys a power law. Additionally, the ground state entanglement entropy reaches a finite value due to the existence of a non-Hermitian correlation length in the non-Hermitian system. Attractive or repulsive interaction drives the system into the PT-symmetry broken regime or protects PT symmetry, respectively.