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arXiv · 2609.03766

Ground-State Phase Diagram, Higher-Winding Topology, and Lifshitz Criticality in an Anisotropic Four-Spin XX Chain

Mohammad Abbasi·Faraz Valeh·Saeed Mahdavifar
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Abstract

We investigate the quantum critical and topological properties of a spin-$1/2$ XX chain with anisotropic four-spin cluster interactions in a transverse magnetic field. The interplay of exchange anisotropy, cluster interactions, and the external field produces a rich phase diagram with multiple gapped topological phases and distinct quantum critical boundaries. We identify several Lifshitz-type transitions arising from reconstructions of the low-energy Fermi-point structure, including an unconventional multicritical point where distinct critical branches intersect and the momentum-space topology undergoes a singular reorganization. In the isotropic limit, a conventional Lifshitz transition emerges through the merging and annihilation of Fermi points, revealing distinct mechanisms of Fermi-point reconstruction within the same model. The gapped phases are characterized by quantized winding numbers $\nu=0,\pm1,-2,$ and $\pm3$, with the higher-winding phases induced by the extended cluster interactions. The $\nu=\pm3$ phases exhibit a richer topological structure than conventional short-range Kitaev-type chains and are separated from other sectors by field- and interaction-driven gap closings. These topological distinctions are further reflected in characteristic degeneracy patterns of the lowest levels of the bulk entanglement spectrum. Our results demonstrate that anisotropic multispin interactions provide a versatile route to realizing higher-winding topological phases and unconventional multicriticality in one-dimensional quantum systems.

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Mohammad Abbasi, Faraz Valeh, Saeed Mahdavifar. 2026-09-03. Ground-State Phase Diagram, Higher-Winding Topology, and Lifshitz Criticality in an Anisotropic Four-Spin XX Chain. https://arxiv.org/abs/2609.03766

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