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Journal of Physics A Mathematical and General

Diagonalization of a coupled supersymmetrict-Jmodel and its ground-state properties

Sooa Park, K Lee

Published Mar 26, 2001• 0 citations
Publisher

Abstract

We obtain an integrable two-leg supersymmetric t - J model through the algebraic Bethe ansatz scheme in the BFF grading. In this model, the two t - J chains interact with each other via a coupling constant κ. The model reduces to a two-chain Heisenberg spin model when the bosonic degrees of freedom are turned off and to two decoupled t - J chains when κ = 0. The construction of the diagonalized Hamiltonian yields the Bethe ansatz equations. We also obtain thermodynamic Bethe ansatz equations and calculate the magnetic susceptibility at a weak magnetic field and at zero temperature.

DOI
10.1088/0305-4470/34/13/310

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We obtain an integrable two-leg supersymmetric t - J model through the algebraic Bethe ansatz scheme in the BFF grading. In this model, the two t - J chains interact with each other via a coupling constant κ. The model reduces to a two-chain Heisenberg spin model when the bosonic degrees of freedom are turned off and to two decoupled t - J chains when κ = 0. The construction of the diagonalized Hamiltonian yields the Bethe ansatz equations. We also obtain thermodynamic Bethe ansatz equations and calculate the magnetic susceptibility at a weak magnetic field and at zero temperature.
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 consider an exactly solvable two-chain quantum spin- model in a generalized form with enhanced spin frustration. This model is exactly diagonalized via Bethe's ansatz. The low-temperature specific heat of the system is obtained with and without a magnetic field, using the thermodynamic Bethe ansatz equations. We also calculate the magnetic susceptibility in a sufficiently weak field, yielding typical logarithmic corrections. The spin frustration affects only the amplitudes in the magnetic susceptibility and the specific heat. This extends the previous results for a simple two-chain quantum spin model to the generalized one.
The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.
The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are derived for the second eigenvalue problem associated with spin degrees of freedom. It is found that the second eigenvalue problem can be transformed to that of the transfer matrix of the inhomogeneous XXX spin chain, which allows us to obtain the spectrum of the Hamiltonian and the associated Bethe ansatz equations by the off-diagonal Bethe ansatz method.