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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 Almas Abbasi, F. Valeh, S. Mahdavifar

Published Jan 1, 2026• 0 citations
arXivHTMLPDF
DOI
10.2139/ssrn.7528947

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Abstract We investigate the ground-state quantum correlations in the spin-1/2 XX chain with anisotropic four-spin interaction (AFSI), employing an exact analytical approach via fermionization. The phase diagram of the system hosts three distinct quantum critical lines that separate non-trivial topological phases characterized by winding numbers ν = ±1 and ν = ±3. To probe the system’s critical behavior and topological nature, we analyze two key quantum correlation measures: concurrence and quantum discord between nearest-neighbor spin pairs. Our results reveal that while concurrence is limited in detecting all critical lines particularly in phases with higher winding numbers, quantum discord successfully identifies all quantum phase transitions, either through cusps or discontinuities in its first derivative. Furthermore, quantum discord assumes larger values in topological phases with lower winding numbers, suggesting that the structure and localization of quantum correlations are influenced by topological order. These findings underscore the effectiveness of quantum discord as a robust diagnostic tool for both criticality and topology in many-body quantum systems. Our results offer valuable insight for advancing correlation-based techniques in quantum information science and highlight the potential role of topological spin chains in future quantum technologies.
We investigate the one-dimensional spin-1/2 XX chain with anisotropic three-spin interactions, which hosts four distinct topological phases separated by critical lines. Using exact fermionization, we analyze the spin squeezing parameter, entanglement entropy, and bulk entanglement spectrum to characterize the ground state. Our results show that the system remains unsqueezed across the entire phase diagram, with maximal unsqueezing at criticality. The entanglement entropy exhibits cusp-like singularities at the critical lines, while the extracted central charges reveal distinct critical behaviors. Furthermore, the lowest level of the bulk entanglement spectrum is four-fold degenerate in two phases and two-fold in the others, reflecting the topological nature of each phase. These findings offer deeper insight into the interplay between topology, criticality, and quantum correlations in low-dimensional spin systems.
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