Non-Hermitian quantum phase transitions in the XY model induced by staggered imaginary Dzyaloshinskii--Moriya interaction

Abstract

We investigate non-Hermitian quantum phase transitions driven by staggered imaginary Dzyaloshinskii--Moriya (DM) interactions in a transverse-field $XY$ chain. By virtue of a staggered nonunitary transformation, we exactly diagonalize the Hamiltonian. For $D<1$, this procedure maps the non-Hermitian model onto a standard Hermitian $XY$ chain, allowing analytical derivation of the full phase boundaries. The parameter line $D=1$ forms an exceptional boundary with coalesced quasiparticle eigenvalues and eigenvectors, while the entire $D>1$ regime falls into the $\mathcal{RT}$-symmetry-broken phase containing two distinct $z$-ferromagnetic phases. We examine common quantum-information probes and show that conventional measures, such as entanglement entropy, quantum discord, and quantum coherence, fail to capture the $\mathcal{RT}$ symmetry-breaking transition. To address this deficiency, we propose a novel coherence measure $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ based on $\mathcal{RT}$ symmetry and complex-conjugate eigenpair correlations. Embedding intrinsic non-Hermitian information of left and right eigenstates, $\widetilde{\mathrm{QC}}_{\max}^{\rm LR}$ reliably identifies the $\mathcal{RT}$ symmetry-breaking transition and accurately resolves all magnetic phase boundaries.