Ground-State Phase Diagram, Higher-Winding Topology, and Lifshitz Criticality in an Anisotropic Four-Spin XX Chain
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 ν=0,±1,−2, and ±3, with the higher-winding phases induced by the extended cluster interactions. The ν=±3 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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BibTeX
@misc{abbasi2026groundstate,
title = {{Ground-State Phase Diagram, Higher-Winding Topology, and Lifshitz Criticality in an Anisotropic Four-Spin XX Chain}},
author = {Mohammad Abbasi and Faraz Valeh and Saeed Mahdavifar},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03766},
eprint = {2609.03766},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03766},
}
RIS
TY - UNPB
TI - Ground-State Phase Diagram, Higher-Winding Topology, and Lifshitz Criticality in an Anisotropic Four-Spin XX Chain
AU - Mohammad Abbasi
AU - Faraz Valeh
AU - Saeed Mahdavifar
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03766
UR - https://arxiv.org/abs/2609.03766
AB - 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 ν=0,±1,−2, and ±3, with the higher-winding phases induced by the extended cluster interactions. The ν=±3 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.
ER -