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arXiv:hep-th/9410070 · Physical Review Letters

Exact Solution of the Simplest Superorthosymplectic Invariant Magnet

Marcio Jose Martins

Published Apr 24, 1995• 18 citations
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Abstract

We present the exact solution of the $\mathrm{Osp}(1|2)$ invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibits a new feature by presenting an explicit and distinct phase behavior in even and odd sectors of the theory. The ground state, the low-lying excitations, and the critical properties are discussed by exploiting the Bethe ansatz solution.

DOI
10.1103/physrevlett.74.3316

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We present the exact solution of the Osp(1∣2)\mathrm{Osp}(1|2)Osp(1∣2) invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibits a new feature by presenting an explicit and distinct phase behavior in even and odd sectors of the theory. The ground state, the low-lying excitations, and the critical properties are discussed by exploiting the Bethe ansatz solution.
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The one-dimensional anisotropic t - J model was exactly solved using the Bethe ansatz . We first discuss the effect of anisotropy on the ground-state properties. We find a continuous phase transition induced by a magnetic field. The low-lying (spin and charge) excitation spectrum is obtained for various fillings. According to the anisotropy, the model has massive or massless modes for spin excitations. At half-filling, the model reduces to the spin- antiferromagnetic XXZ -model. We calculate the correct excitation continuum whose lowest mode is lower than that obtained by des Cloizeaux and Gaudin. Charge excitations are massless for any value of the anisotropy.
The supersymmetric $t\text{\ensuremath{-}}J$ model with boundary hopping integrals and fields is proposed and solved exactly by means of the Bethe ansatz method. We find that for certain values of the boundary hopping integrals and fields the ground state contains boundary bound states, as new solutions of the Bethe ansatz equations in a charge sector called boundary charge strings. The boundary states define the thermodynamic properties of the boundary, such as the boundary charge, magnetic moment, that have been calculated numerically as a function of the magnetic field and chemical potential. We show that the boundary charge strings lead to a logarithmic divergent behavior of boundary magnetic moment in a weak magnetic field limit.