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.
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.
In this paper, we investigate the ground state properties of the spin-1/2 XX chain model with anisotropic three-spin interaction using the fermionization technique. By exactly diagonalizing the Hamiltonian, we analyze the dispersion relation, ground state energy, and order parameters. Our findings identify two gapless phases, distinguished by a Lifshitz transition line: one exhibiting long-range chiral correlations and the other characterized by chiral-nematic correlations. These correlations do not correspond to conventional symmetry-breaking local order parameters typically associated with gapped one-dimensional phases but instead signify emergent quantum coherence in the gapless regime. Further, we study the ground state phase diagram through the concurrence and quantum discord between nearest-neighbor spins, finding that these measures are maximized at the critical line, with an additional entangled region observed. Finally, we examine the spin squeezing parameter and entanglement entropy, demonstrating that the ground state is squeezed throughout and becomes extremely squeezed at the critical line. Notably, in the gapless chiral-nematic phase, the Heisenberg limit is achieved. By dividing the system into two equal parts, we observe significant entanglement in the gapless chiral phase. The central charge calculation confirms the critical nature of the gapless chiral-nematic phase, while the entanglement entropy follows volume-law scaling in the gapless chiral phase.
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.
ABSTRACT In this study, we investigate the emergence of non‐trivial topological phases in a 1D spin‐1/2 XX model induced by anisotropic four‐spin interactions. By employing the fermionization technique, we precisely diagonalize the system's Hamiltonian and analytically identify three critical lines. Subsequently, we calculate the energy gap, fidelity susceptibility, cluster local order parameters, winding number, and entanglement spectrum. Our findings identify three crucial boundaries that divide five gapped phases, each characterized by the coexistence of symmetry‐protected topological order and spontaneous symmetry breaking. Analyzing the winding number as a topological invariant allows us to distinguish these gapped phases as distinct non‐trivial topological phases, characterized by integer values of . Moreover, we observe topological phase transitions at quantum critical points, where the winding number changes are associated with the closing and reopening of the energy gap. Furthermore, we demonstrate that for a given winding number , the degeneracy of the lowest eigenvalue in the entanglement spectrum is generally . This work provides novel insights into the role of anisotropic four‐spin interactions in driving topological phenomena in low‐dimensional quantum systems, offering a deeper understanding of the interplay between topology and quantum fluctuations.
Entangled spin coherent states are a type of quantum states that involve two or more spin systems that are correlated in a nonclassical way. These states can improve metrology and information processing, as they can surpass the standard quantum limit, which is the ultimate bound for precision measurements using coherent states. However, finding entangled coherent states in physical systems is challenging because they require precise control and manipulation of the interactions between the modes. In this work we show that entangled unique coherent states can be found in the ground state of the spin-1/2 XX chain model with three-spin interaction, which is an exactly solvable model in quantum magnetism. We use the spin squeezing parameter, the l_{1}-norm of coherence, and the entanglement entropy as tools to detect and characterize these unique coherent states. We find that these unique coherent states exist in a gapless spin liquid phase, where they form a line that separates two regions with different degrees of squeezing. We call this line the entangled unique coherent line, as it corresponds to the almost maximum entanglement between two halves of the system. We also study the critical scaling of the spin squeezing parameter and the entanglement entropy versus the system size.
Quantum entanglement can be an effective diagnostic tool for probing topological phases protected by global symmetries. Recently, the notion of nontrivial topology in critical systems has been proposed and is attracting growing attention. In this work, as a concrete example, we explore the quantum entanglement properties of fermionic symmetry-enriched quantum critical points by constructing exactly solvable models based on stacked multiple Kitaev chains. We first analytically establish the global phase diagram using entanglement entropy and reveal three topologically distinct gapped phases with different winding numbers, along with three topologically distinct transition lines separating them. Importantly, we unambiguously demonstrate that two transition lines exhibit fundamentally different topological properties despite sharing the same central charge. Specifically, they display nontrivial topological degeneracy in the entanglement spectrum under periodic boundary conditions, thereby generalizing the Li-Haldane bulk-boundary correspondence to a broader class of fermionic symmetry-enriched criticality. Additionally, we identify a novel Lifshitz multicritical point at the intersection of the three transition lines, which also exhibits nontrivial topological degeneracy. This work provides a valuable reference for investigating gapless topological phases of matter from the perspective of quantum entanglement.
We investigate the ground-state phase diagram of a frustrated spin-1/2 Heisenberg ladder in the transverse magnetic field with an anisotropic inter-rung exchange coupling α. This bond-anisotropic parameter continuously interpolates among the Ising-like limit α=0, the isotropic point α=1, and the XY-dominated regime α≫1. Using density-matrix renormalization group calculations within a matrix-product-state framework, we analyze bipartite entanglement, magnetization, and spin correlations to characterize the emergent quantum phases. We identify six distinct ground-state phases, including rung-singlet, Haldane-like, Tomonaga-Luttinger liquid, canted Ising-ordered, XY-polarized, and ordered ferromagnetic states. While magnetization and local correlations provide a first insight into phase classifications, the finite-size scaling of the entanglement measures offers a more sensitive and unified diagnostics of both gapped and gapless regimes. In the gapless regime, we extract the central charge c≃1, confirming Tomonaga-Luttinger liquid behavior, while at the transition between the canted Ising and ferromagnetic phases, we observe c≃1/2, consistent with the Ising universality. Finally, we find that both the Haldane-like behavior and the extended critical Tomonaga-Luttinger liquid regime are strongly confined to the vicinity of the isotropic point α=1.