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Interdisciplinary Information Sciences

Ground State Properties of One-Dimensional Quantum Chiral XY-Model.

Yoshihiko Fukui, Tsuyoshi Horiguchi

Published Jan 1, 2000• 5 citations
Publisher

Abstract

We investigate ground state properties of a one-dimensional quantum chiral XY -model in a magnetic field. Numerical calculations are carried out by using a method of density matrix renormalization group. We also analyze behaviors of perturbation series for the ground state energy. For a special case that the natural cantedness is π⁄2, a value of the critical magnetic field for saturation of magnetization is shown to be given exactly in terms of the smallest zero of the Bessel function J0(x ). We obtain the ground state phase diagram.

DOI
10.4036/iis.2000.57

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We investigate ground state properties of a one-dimensional quantum chiral XY -model in a magnetic field. Numerical calculations are carried out by using a method of density matrix renormalization group. We also analyze behaviors of perturbation series for the ground state energy. For a special case that the natural cantedness is π⁄2, a value of the critical magnetic field for saturation of magnetization is shown to be given exactly in terms of the smallest zero of the Bessel function J0(x ). We obtain the ground state phase diagram.
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The spin-1/2 quantum anisotropic XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.
The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.
The spin-1/2 quantum anisotropic XY\mathrm{XY}XY spin chain in a transverse random magnetic field parallel to the z axis is numerically studied by means of the density-matrix renormalization group. The dependence of the spontaneous magnetization and the energy gap on both the strength of the random magnetic field and the factor of anisotropy is determined. The critical line for the order-disorder phase transition is obtained and the resulting phase diagram is drawn. Our results are compatible with the fact that models with different factors of anisotropy fall within the same universality class as the quantum Ising model in a transverse random field.
Starting with the known exact solution of the one-dimensional supersymmetric t-J model, the authors investigate ground-state properties of the system in the presence of an external magnetic field. By analytical calculations they find a representation of the magnetization curves and the susceptibility using the dressed charge matrix and the charge and spin densities: the dressed properties are given by a set of coupled integral equations which are derived from the Bethe ansatz equations in the thermodynamic limit. Some special results are found analytically, namely the magnetic field at which saturation occurs and the corresponding susceptibility. Furthermore they show the vanishing of the lower critical field. The dependence of magnetization and susceptibility on the magnetic field is calculated numerically for various particle densities.
We clarify the finite temperature properties of a chiral XY-model by calculating the free energy, the entropy, the specific heat, the correlation functions and so on, by using numerical solutions of an integral equation. The specific heat has a small peak in a lower-temperature side of the main peak for the system in which the period of ground-state configuration is 1 or 4. The information stored in the ground-state configuration is disturbed easily by the temperature when the configuration is not stable. The critical behavior of the correlation length is either of the XY type or of the Ising type according to whether or not the ground-state configuration has a long period.