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This research advances the theoretical understanding of non-Hermitian quantum systems by introducing a novel coherence measure capable of detecting symmetry-breaking transitions invisible to standard entanglement metrics. By exactly diagonalizing a specific Hamiltonian model, the study provides analytical phase boundaries that are critical for developing robust quantum simulation protocols and error correction strategies in future hardware.
Non-Hermitian quantum phase transitions in the XY model induced by staggered imaginary Dzyaloshinskii--Moriya interaction
arXiv:2609.23721v1 Announce Type: new 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 $D1$ 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.
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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2609.23721 [quant-ph]
(or arXiv:2609.23721v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.23721 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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