Thermodynamic Bethe ansatz equation for osp(1|2) integrable spin chain

The thermodynamic Bethe ansatz is applied to a quantum integrable spin chain associated with the Lie superalgebra osp(1|2). Using the string hypothesis, we derive a set of infinite number of non-linear integral equations (thermodynamic Bethe ansatz equation), which characterize the free energy. The low temperature limit of the free energy is also discussed. Modern Physics Letters A, in press. Solvable lattice models related to Lie superalgebras [1] have received much attentions [2, 3, 4, 5, 6, 7, 8, 9]. Characteristically, these models possess both fermionic and bosonic degree of freedom and their Boltzmann weights (Rmatrices) satisfy the graded Yang-Baxter equations[2]. Some of them include well-known models as special cases. For example, supersymmetric t− J model is related to the Lie superalgebra sl(1|2). To analyze such models, Bethe ansatz is often used (See for example [3, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28] and references therein). Moreover, thermodynamics have been discussed by several people. In particular, the thermodynamic Bethe ansatz (TBA) equation was given for the supersymmetric t − J model [10, 26] and the supersymmetric extended Hubbard model [14, 26], which is related to sl(2|2). More recently, the TBA equation for sl(r|s) model was discussed [28] in relation with the continuum limit of integrable spin chains. However, in contrast to sl(r|s) case, the thermodynamics of quantum spin chain related to the orthosymplectic Lie superalgebra osp(r|2s) is not much understood. In particular, to the author’s knowledge, there is no literature on the thermodynamic Bethe ansatz (TBA) equation even for the simplest orthosymplectic osp(1|2) integrable spin chain [3, 4, 5, 7, 8, 9, 16, 17]. This is regrettable e-mail address: [email protected] JSPS Research Fellow; e-mail address: [email protected]