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This study provides a rigorous theoretical framework for using Lee-Yang zero topology to map quantum phase diagrams in modulated spin chains with Dzyaloshinskii-Moriya interactions. By linking complex zero contours directly to band folding and critical fields, the work offers new analytical tools for identifying gapless chiral phases in quasiperiodic systems. Such insights are relevant for designing robust quantum materials and understanding topological transitions in non-equilibrium quantum matter.
Lee-Yang zeros of modulated XY spin chains with Dzyaloshinskii-Moriya interaction: zero-contour topology and quantum phase-diagram reconstruction
arXiv:2609.05469v1 Announce Type: new Abstract: We investigate the Lee--Yang zeros (LYZ) of inhomogeneous anisotropic XY spin chains with Dzyaloshinskii--Moriya (DM) interactions in the complex transverse-field plane, focusing on their fundamental connection to quantum phase transitions. We systematically study uniform chains, period-2 and period-3 modulated chains, and Fibonacci quasiperiodic chains of lengths 5 and 8. As the DM coupling strength $D$ increases, the LYZ exhibit qualitatively distinct topological evolutions on the complex plane: the complex zeros of the uniform chain collapse toward the real axis; periodic chains feature either bifurcation of closed zero contours before all zeros become real or a single re-emergence of complex zeros; quasiperiodic chains exhibit repeated annihilation and revival of complex zeros. Analytical derivations demonstrate that this diverse behavior originates from DM-induced shifts of folded bands and the modulation of zero positions by anisotropic pairing at particle--hole band crossings. Our results establish a direct correspondence between LYZ topology and band deformation: isolated contact points of zeros with the real axis correspond to discrete quantum critical fields, while continuous real-zero intervals directly identify gapless chiral phases. Accordingly, beyond locating phase boundaries, LYZ can distinguish characteristic phases and serve as an intuitive probe for band folding and phase diagram restructuring.
Abstract:We investigate the Lee--Yang zeros (LYZ) of inhomogeneous anisotropic XY spin chains with Dzyaloshinskii--Moriya (DM) interactions in the complex transverse-field plane, focusing on their fundamental connection to quantum phase transitions. We systematically study uniform chains, period-2 and period-3 modulated chains, and Fibonacci quasiperiodic chains of lengths 5 and 8. As the DM coupling strength $D$ increases, the LYZ exhibit qualitatively distinct topological evolutions on the complex plane: the complex zeros of the uniform chain collapse toward the real axis; periodic chains feature either bifurcation of closed zero contours before all zeros become real or a single re-emergence of complex zeros; quasiperiodic chains exhibit repeated annihilation and revival of complex zeros. Analytical derivations demonstrate that this diverse behavior originates from DM-induced shifts of folded bands and the modulation of zero positions by anisotropic pairing at particle--hole band crossings. Our results establish a direct correspondence between LYZ topology and band deformation: isolated contact points of zeros with the real axis correspond to discrete quantum critical fields, while continuous real-zero intervals directly identify gapless chiral phases. Accordingly, beyond locating phase boundaries, LYZ can distinguish characteristic phases and serve as an intuitive probe for band folding and phase diagram restructuring.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2609.05469 [quant-ph]
(or arXiv:2609.05469v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.05469 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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