Non-Hermitian quantum system generated from two coupled Sachdev-Ye-Kitaev models

TL;DR

This paper demonstrates that a non-Hermitian two coupled SYK model shares thermodynamic properties with its Hermitian counterpart, with unique biorthogonal ground states and energy spectrum unaffected by non-Hermiticity.

Contribution

It introduces a non-Hermitian coupled SYK model that preserves thermodynamic structure and reveals novel biorthogonal ground states tunable via non-Hermiticity.

Findings

Energy spectrum unaffected by non-Hermiticity

Ground state entanglement remains consistent

Free energy independent of non-Hermiticity

Abstract

We show that a non-Hermitian two coupled Sachdev-Ye-Kitaev (SYK) model can provide thermodynamic structure equivalent to Hermitian two coupled SYK model. The energy spectrum, the entanglement degree of the ground states and the low energy effective action of this model are not influenced by the non-Hermiticity. The novel biorthogonal ground states demonstrates that two SYK sites, one of which can be in the ground state and the other in the Schwarzian excited state by tuning the non-Hermiticity. We find evidence that the free energy is independent of the non-Hermiticity.