Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry

TL;DR

This paper explores a non-Hermitian anisotropic XY spin model with intrinsic rotation-time reversal symmetry, revealing real spectra under certain conditions and identifying exceptional points that delineate symmetry phases, thus advancing understanding of complex quantum mechanics.

Contribution

It introduces a non-Hermitian anisotropic XY model with RT symmetry, providing exact solutions and characterizing exceptional points in the phase diagram.

Findings

Real spectrum occurs when eigenvectors are RT symmetric.

Exceptional points form a hyperbola in the thermodynamic limit.

The model offers insights into complex quantum mechanics for spin systems.

Abstract

We systematically study the non-Hermitian version of the one-dimensional anisotropic XY model, which in its original form, is a unique exactly solvable quantum spin model for understanding the quantum phase transition. The distinguishing features of this model are that it has full real spectrum if all the eigenvectors are intrinsic rotation-time reversal (RT) symmetric rather than parity-time reversal (PT) symmetric, and that its Hermitian counterpart is shown approximately to be an experimentally accessible system, an isotropic XY spin chain with nearest neighbor coupling. Based on the exact solution, exceptional points which separated the unbroken and broken symmetry regions are obtained and lie on a hyperbola in the thermodynamic limit. It provides a nice paradigm to elucidate the complex quantum mechanics theory for a quantum spin system.