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Physical review. B, Condensed matter

Higher conservation laws and algebraic BetheAnsätzefor the supersymmetrict-Jmodel

Fabian H. L. Eßler, V. E. Korepin

Published Oct 1, 1992• 252 citations
Publisher

Abstract

We construct the enveloping fundamental spin model of the t-J Hamiltonian using the quantum-inverse-scattering method (QISM), and present all three possible algebraic Bethe Ansa$iuml---tze. Two of the solutions have been previously obtained in the framework of the coordinate-space Bethe Ansatz by Sutherland and by Schlottmann and Lai, whereas the third solution is new. The formulation of the model in terms of the QISM enables us to derive explicit expressions for higher conservation laws.

DOI
10.1103/physrevb.46.9147

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We construct the enveloping fundamental spin model of the t-J Hamiltonian using the quantum-inverse-scattering method (QISM), and present all three possible algebraic Bethe Ansa$iuml---tze. Two of the solutions have been previously obtained in the framework of the coordinate-space Bethe Ansatz by Sutherland and by Schlottmann and Lai, whereas the third solution is new. The formulation of the model in terms of the QISM enables us to derive explicit expressions for higher conservation laws.
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.
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and find an unexpected and remarkable applications in quantum inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter algebras the standard procedure of QISM one obtains new wide classes of quantum models which, being integrable (i.e. having enough number of commuting integrals of motion) are only quasi-exactly solvable (i.e. admit an algebraic Bethe ansatz solution for arbitrarily large but limited parts of the spectrum). These quasi-exactly solvable models naturally arise as deformations of known exactly solvable ones. A general theory of such deformations is proposed. The correspondence ``Yangian --- quasi-Yangian'' and ``XXXXXXXXX spin models --- quasi-XXXXXXXXX spin models'' is discussed in detail. We also construct the classical conterparts of quasi-Yang-Baxter algebras and show that they naturally lead to new classes of classical integrable models. We conjecture that these models are quasi-exactly solvable in the sense of classical inverse scattering method, i.e. admit only partial construction of action-angle variables.