Ring-Frustrated Non-Hermitian $XY$ Model

TL;DR

This paper investigates a non-Hermitian XY spin chain with an odd number of sites, revealing real energy spectra, a unique ground state with a kink-like excitation, and non-trivial topological properties.

Contribution

It introduces a non-Hermitian XY model with odd sites, identifying a novel ground state and topological kink phase not seen in previous models.

Findings

Real energy spectrum in certain parameter regions

Ground state with one mode occupied, not vacuum

Presence of a topologically non-trivial kink phase

Abstract

We study a non-Hermitian version of XY closed chain with odd number of lattice sites. We consider both anti-ferromagnetic coupling and also a symmetric non-collinear spin coupling. It is found that the energy spectrum is real in certain region of the parameter space. In contrast to previous non-Hermitian models, the ground state is a state with one mode occupied inside this real energy spectrum region, instead of the artificially identified vacuum state. At the same time, there appears a gapless excitation, which is made by kink like spin configurations. It is also found that this kink phase has non-trivial topological invariant.