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arXiv:2609.05469

Lee-Yang zeros of modulated XY spin chains with Dzyaloshinskii-Moriya interaction: zero-contour topology and quantum phase-diagram reconstruction

Hong Jiang, Xiang-Ping Jiang, Yan-Chao Li

quant-phcond-mat.stat-mechSubmitted Aug 20, 2026• Announced Aug 21, 2026• 0 citations
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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.

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Acta Physica Sinica•Jan 1, 2018•5 citations
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 DDD 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.
The partition function zeros of the anisotropic XY chain in a complex transverse field are studied analytically and numerically. It is found that the partition function zeros of the periodic and quasiperiodic quantum Ising chain lie on the circle at zero temperature and the radius equal to the values of the critical field. For the periodic and quasiperiodic anisotropic XY chains, the closed curves are split to two or three closed curves as the anisotropic parameter gamma decreases at a given ratio of two kinds of exchange interactions. For the isotropic XX case, the partition function zeros lie on the straight segments which are parallel to the real axis and the segments move towards the real axis as the temperature goes to zero.
Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XYXYXY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, $\ensuremath{\lambda}$ corresponding to XYXYXY anisotropy, and DDD corresponding to the strength of DM interaction. The flow portrait of the model is governed by two global Ising-Kitaev attractors at $(\ensuremath{\lambda}=\ifmmode\pm\else\textpm\fi{}1,D=0)$ and a repeller line, $\ensuremath{\lambda}=0$. This line itself is characterized by an attractor at D=0D=0D=0. Renormalization flow of concurrence suggests that the $\ensuremath{\lambda}=0$ line corresponds to a topological phase transition. The gap starts at zero on this repeller line corresponding to superfluid phase of underlying bosons; and flows towards a finite value at the Ising-Kitaev points. At these two fixed points the spin fields become purely classical, and hence the resulting Ising degeneracy can be interpreted as topological degeneracy of dual degrees of freedom. The state of affairs at the Ising-Kitaev fixed point is consistent with the picture of a ppp-wave pairing of strength $\ensuremath{\lambda}$ of Jordan-Wigner fermions coupled with Chern-Simons gauge fields.
We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with uniform and alternating transverse magnetic fields (ATXY) in the presence of the Dzyaloshinskii-Moriya (DM) interaction by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field (UXY), which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show the appearance of a new gapless chiral phase---in the XY model with uniform as well as alternating field. We further observe that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also find that the factorization surface at zero temperature present in this model without DM interaction becomes a volume on the introduction of the latter. Moreover, DM interaction turns out to be good to generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system.
We investigate the phase diagram of a non-Hermitian XY chain with staggered Dzyaloshinskii--Moriya (DM) interactions using quantum-information methods. Through an alternating local-spin-rotation transformation, the model is mapped onto a standard DM-free XY chain, and the resulting transformed Hamiltonian exhibits rotation--time-reversal ($\RT$) symmetry. Combining correlation-function analysis with known phase results of the standard XY chain, we construct the phase diagram for the present system. We further adopt quantum-information-based quantities to systematically assess their performance in characterizing quantum phase transitions within this non-Hermitian system. Our results show that single-site entanglement can only detect the Luttinger-liquid (LL)--paramagnetic (PM) phase transition, which corresponds to the exceptional boundary across which $\RT$ symmetry is restored. In contrast, quantum discord (QD) and quantum coherence (QC) identify both phase boundaries: in addition to locating the exceptional boundary, their second-order derivatives resolve the ferromagnetic (FM)--LL transition inside the $\RT$-broken region. Moreover, measurements of QC along different directions capture the DM-induced relative rotation between the two sublattices, thereby distinguishing the staggered-DM chain from a zero-DM chain with identical effective parameters.
In this paper, we study the quantum coherence of one-dimensional transverse XY model with Dzyaloshinskii-Moriya interaction, which is given by the following Hamiltonian:HXY=∑i=1N((1+γ/2) σixσi+1x+(1-γ/2) σiyσi+1y-hσiz) ∑i=1ND(σixσi+1y-σiyσi+1x).(8)Here, 0 ≤ γ ≤ 1 is the anisotropic parameter, h is the magnitude of the transverse magnetic field, D is the strength of Dzyaloshinskii-Moriya (DM) interaction along the z direction. The limiting cases such as γ=0 and 1 reduce to the isotropic XX model and the Ising model, respectively. We use the Jordan-Winger transform to map explicitly spin operators into spinless fermion operators, and then adopt the discrete Fourier transform and the Bogoliubov transform to solve the Hamiltonian Eq.(8) analytically. When the DM interactions appear, the excitation spectrum becomes asymmetric in the momentum space and is not always positive, and thus a gapless chiral phase is induced. Based on the exact solutions, three phases are identified by varying the parameters:antiferromagnetic phase, paramagnetic phase, and gapless chiral phase. The antiferromagnetic phase is characterized by the dominant x-component nearest correlation function, while the paramagnetic phase can be characterized by the z component of spin correlation function. The two-site correlation functions Grxy and Gryx (r is the distance between two sites) are nonvanishing in the gapless chiral phase, and they act as good order parameters to identify this phase. The critical lines correspond to h=1, γ=2D, and h=√4D2 -γ2 + 1 for γ>0. When γ=0, there is no antiferromagnetic phase. We also find that the correlation functions undergo a rapid change across the quantum critical points, which can be pinpointed by the first-order derivative. In addition, Grxy decreases oscillatingly with the increase of distance r. The correlation function Grxy for γ=0 oscillates more dramatically than for γ=1. The upper boundary of the envelope is approximated as Grxy~r-1/2, and the lower boundary is approximately Grxy~r-3/2, so the long-range order is absent in the gapless chiral phase. Besides, we study various quantum coherence measures to quantify the quantum correlations of Eq.(8). One finds that the relative entropy CRE and the Jensen-Shannon entropy CJS are able to capture the quantum phase transitions, and quantum critical points are readily discriminated by their first derivative. We conclude that both quantum coherence measures can well signify the second-order quantum phase transitions. Moreover, we also point out a few differences in deriving the correlation functions and the associated density matrix in systems with broken reflection symmetry.