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Scientific Reports

Hybrid critical line in the spin-1/2 XX chain with gamma interaction under transverse fields

M. Abbasi, S. Mahdavifar, Mostafa Motamedifar

Published Jul 1, 2025• 4 citations
Publisher

Abstract

We investigate the spin-1/2 XX chain with uniform Gamma interaction under a transverse magnetic field. By exactly diagonalizing the Hamiltonian using the Fermionization technique, we rigorously analyze the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Additionally, we thoroughly examine various order parameters, including magnetization, staggered magnetization, chirality, and spin nematicity, which delineate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order. Notably, we identify a hybrid critical line in the ground state phase diagram. This hybrid critical line is defined as a line where multiple types of phase transitions converge. At points along this line, the system exhibits behaviors characteristic of different types of critical points simultaneously. Understanding the magnetic properties under different field conditions can lead to the development of new magnetic materials and technologies. Our results provide a framework for experimentally manipulating magnetic fields, allowing researchers to control and observe changes in material properties. This, in turn, offers valuable insights into the fundamental physics governing these systems.

DOI
10.1038/s41598-025-05220-9

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We investigate the spin-1/2 XX chain with uniform Gamma interaction under a transverse magnetic field. By exactly diagonalizing the Hamiltonian using the Fermionization technique, we rigorously analyze the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Additionally, we thoroughly examine various order parameters, including magnetization, staggered magnetization, chirality, and spin nematicity, which delineate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order. Notably, we identify a hybrid critical line in the ground state phase diagram. This hybrid critical line is defined as a line where multiple types of phase transitions converge. At points along this line, the system exhibits behaviors characteristic of different types of critical points simultaneously. Understanding the magnetic properties under different field conditions can lead to the development of new magnetic materials and technologies. Our results provide a framework for experimentally manipulating magnetic fields, allowing researchers to control and observe changes in material properties. This, in turn, offers valuable insights into the fundamental physics governing these systems.
In this study, we delve into the intricate ground state phase diagram of anisotropic spin-1/2 XXZ chains under the uniform Gamma interaction. Employing the robust infinite time evolving block decimation (iTEBD) technique and the Lanczos technique, we meticulously obtain the model's ground state properties. Complementing our numerical analysis, we derive analytical approximations through a mean-field framework, transposed into the fermionic representation. Our investigation rigorously scrutinizes the energy spectrum, distinguishing between gapped and gapless domains at absolute zero. Furthermore, we thoroughly examine various order parameters including magnetization, staggered magnetization, chirality, and spin nematicity, which demarcate the diverse phases within the ground state phase diagram, each characterized by its unique long-range order.
We study the spin-1/2 XX chain with a modulated Gamma interaction (GI), which results from the superposition of uniform and staggered Gamma terms. We diagonalize the Hamiltonian of the model exactly using the Fermionization technique. We then probe the energy gap and identify the gapped and gapless regions. We also examine the staggered chiral, staggered nematic and dimer order parameters to determine the different phases of the ground state phase diagram with their respective long-range orders. Our findings indicate that the model undergoes first-order, second-order, gapless-gapless, and gapped-gapped phase transitions.
We consider the spin-1/2 XX chain model with uniform Gamma interaction, exactly solvable using the fermionization approach. The ground state phase diagram reveals two regions: a composite gapless phase and a single gapped phase, separated by a second-order critical line. Within the composite phase, a special line is identified where one coexisting phase vanishes, leaving a single gapless phase. By examining the concurrence and quantum discord (QD) between nearest-neighbor spin pairs, we probe the ground state phase diagram. Our results highlight a discontinuity along the quantum critical line, indicating the phase transition. The special line in the gapless region is detected through concurrence and QD results, showing the sensitivity of these quantum correlations to system parameter changes. We also explore the scaling behavior of concurrence and QD near the quantum critical line, providing insights into the system's critical properties. Furthermore, we identify a line within the gapped phase where both concurrence and QD vanish. Investigating the density matrix along this line, we assess whether the zero QD condition adheres to a novel criterion for arbitrary bipartite states. Our findings indicate that without Heisenberg interaction, the criterion is not met, but with both Heisenberg interaction and Gamma interaction, the criterion for zero QD is satisfied.
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 study the spin-1/2 Kitaev chain with additional XX and symmetric off-diagonal Gamma interactions. By combining the Jordan–Wigner transformation with density matrix renormalization group (DMRG) numerical simulations, we obtain the exact solution of the model and map out the phase diagram containing six distinct phases. The four gapped phases display ferromagnetic and antiferromagnetic magnetic orders along the (1,1,0)- and (1,-1,0)-spin directions, whereas in the gapless phases, the low-energy spectrum consists of two branches of helical Majorana fermions with unequal velocities. The transition lines separating different phases include deconfined quantum critical lines with dynamical critical exponent z = 1 and quadratic critical lines with z = 2. Our work reveals the rich interplay among symmetry, magnetic order, and quantum criticality in the Kitaev–XX–Gamma chain.
We investigate a transverse-field Ising chain with dimerized anisotropic Gamma interactions and demonstrate that, both in the absence and presence of Ising interactions, the competition between Gamma anisotropy and the transverse field gives rise to vector chiral order and dynamical quantum phase transitions. The phase diagram comprises positive and negative vector chiral phases and a paramagnetic phase, characterized by the vector spin chirality and the vector chiral order parameter. In the absence of Ising interactions, we identify a gapless critical line that exhibits no finite-size drift, along which the spin-spin correlations and subsystem entanglement entropy display behavior distinct from that of Ising criticality. Furthermore, we find that the critical times of dynamical quantum phase transitions form periodic or aperiodic sequences, depending on the quench path. Our findings highlight how dimerized off-diagonal exchange enriches both equilibrium ordering and dynamical critical behavior in a quantum Ising chain.