Integral equations for thermodynamics of the osp(1|2s) integrable spin chain

We propose a system of nonlinear integral equations (NLIE), which gives the free energy of the osp(1|2s) integrable spin chain at finite temperatures. In contrast with usual thermodynamic Bethe ansatz equations, our new NLIE contain only a finite number of unknown functions. On deriving NLIE, we use our osp(1|2s) version of the T-system and the quantum transfer matrix method. Based on our NLIE, we also calculate the high temperature expansion of the free energy and the specific heat.Comment: 13 pages, 1 figure, to appear in Phys. Lett. B 544 (2002) 222-23

Quantum groups, Yang-Baxter maps and quasi-determinants

For any quasi-triangular Hopf algebra, there exists the universal R-matrix, which satisfies the Yang-Baxter equation. It is known that the adjoint action of the universal R-matrix on the elements of the tensor square of the algebra constitutes a quantum Yang-Baxter map, which satisfies the set-theoretic Yang-Baxter equation. The map has a zero curvature representation among L-operators defined as images of the universal R-matrix. We find that the zero curvature representation can be solved by the Gauss decomposition of a product of L-operators. Thereby obtained a quasi-determinant expression of the quantum Yang-Baxter map associated with the quantum algebra $U_{q}(gl(n))$. Moreover, the map is identified with products of quasi-Pl\"{u}cker coordinates over a matrix composed of the L-operators. We also consider the quasi-classical limit, where the underlying quantum algebra reduces to a Poisson algebra. The quasi-determinant expression of the quantum Yang-Baxter map reduces to ratios of determinants, which give a new expression of a classical Yang-Baxter map.Comment: 46 page

Determining equations for higher-order decompositions of exponential operators

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.Comment: 30 page