Non-Hermitian spin chains with inhomogeneous coupling

TL;DR

This paper investigates non-Hermitian inhomogeneous spin chains, identifying conditions for real spectra and constructing a universal, non-dynamical metric operator to establish their quasi-Hermiticity, applicable to various integrable models.

Contribution

It introduces a universal, non-dynamical metric operator for non-Hermitian spin chains, extending the understanding of quasi-Hermiticity in inhomogeneous models.

Findings

Identified parameter ranges for real spectra in specific spin chains

Constructed a universal metric operator ensuring quasi-Hermiticity

Applicable to all known homogeneous U_q(sl_2)-invariant integrable chains

Abstract

An open U_q(sl_2)-invariant spin chain of spin S and length N with inhomogeneous coupling is investigated as an example of a non-Hermitian (quasi-Hermitian) model. For several particular cases of such a chain, the ranges of the deformation parameter gamma are determined for which the spectrum of the model is real. For a certain range of gamma, a universal metric operator is constructed and thus the quasi-Hermiticity of the model is established. The constructed metric operator is non-dynamical, its structure is determined only by the symmetry of the model. The results apply, in particular, to all known homogeneous U_q(sl_2)-invariant integrable spin chains with nearest-neighbour interaction. In addition, the most general form of a metric operator for a quasi-Hermitian operator in finite dimensional space is discussed.