Spontaneous PT symmetry breaking and quantum phase transitions in dimerized spin chains

TL;DR

This paper investigates how spontaneous PT symmetry breaking occurs in a non-Hermitian dimerized spin chain with an imaginary magnetic field, revealing conditions for real spectra and phase transitions related to dimerization.

Contribution

It demonstrates that dimerization enables real spectra in non-Hermitian spin chains and explores how to replicate these phases in Hermitian systems through coupling renormalization.

Findings

Real spectra occur only with dimerization.

PT symmetry breaking relates to magnetic field and dimerization.

Phase diagrams can be mimicked by coupling renormalization.

Abstract

The occurrence of parity-time reversal ($\mathcal{PT}$) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full real spectrum, which occurs if and only if all the eigenvectors are $\mathcal{PT}$ symmetric, can appear only in presence of dimerization, i.e. only if the hopping amplitudes between nearest-neighbor spins assume alternate values along the chain. In order to make a connection between such system and the Hermitian world, we study the critical magnetic properties of the model and look for the conditions that would allow to observe the same phase diagram in the absence of the imaginary field. Such procedure amounts to renormalizing the spin-spin coupling amplitudes.