Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model

TL;DR

This paper introduces a non-Hermitian BCS model with exact solutions showing two quantum critical lines of deconfined excitations obeying generalized exclusion statistics, with real spectra on these lines.

Contribution

It presents a novel non-Hermitian BCS Hamiltonian with exact Bethe ansatz solutions revealing quantum critical lines and deconfined excitations with generalized exclusion statistics.

Findings

Two quantum critical lines of deconfined excitations identified.

Real spectra occur precisely on the critical lines.

The critical lines are invariant under renormalization group transformations.

Abstract

We present a pairing Hamiltonian of the Bardeen-Cooper-Schrieffer form which exhibits two quantum critical lines of deconfined excitations. This conclusion is drawn using the exact Bethe ansatz equations of the model which admit a class of simple, analytic solutions. The deconfined excitations obey generalised exclusion statistics. A notable property of the Hamiltonian is that it is non-hermitian. Although it does not have a real spectrum for all choices of coupling parameters, we provide a rigorous argument to establish that real spectra occur on the critical lines. The critical lines are found to be invariant under a renormalisation group map.