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Scientific Reports

Anisotropic spin-1/2 XXZ chains with uniform gamma interaction

S. Mahdavifar, D. C. Liu

Published Dec 3, 2024• 11 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-024-81404-z

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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 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.
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.
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.
The ground-state phase diagram of frustrated S=1 XXZ spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied using the infinite-system density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ_l = S_l^xS_{l+1}^y-S_l^yS_{l+1}^x, whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for Δ< 0.95, where Δis an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.
We study quantum phase transitions of a XXZ spin model with spin S = 1/2 and 1 in one dimension. The XXZ spin chain is one of basic models in understanding various one-dimensional magnetic materials. To study this model, we construct infinite-lattice matrix product state (iMPS), which is a tensor product form for a one-dimensional many-body quantum wave function. By using timeevolution- block-decimation method (TEBD) on iMPS, we obtain the ground states of the XXZ model at zero temperature. This method is very delicate in calculating ground states so that we developed a reliable method of finding the ground state with the dimension of entanglement coefficients up to 300, which is beyond the previous works. By analyzing ground-state energies, half-chain entanglement entropies, and entanglement spectrum, we found the signatures of quantum phase transitions between ferromagnetic phase, XY phase, Haldane phase, and antiferromagnetic phase.
We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.