Analytical results for the Coqblin-Schrieffer model with generalized magnetic fields

Using the approach alternative to the traditional Thermodynamic Bethe Ansatz, we derive analytical expressions for the free energy of Coqblin-Schrieffer model with arbitrary magnetic and crystal fields. In Appendix we discuss two concrete examples including the field generated crossover from the SU(4) to the SU(2) symmetry in the SU(4)-symmetric model.Comment: 5 page

Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory

In this paper we study the Yang-Baxter integrable structure of Conformal Field Theories with extended conformal symmetry generated by the W_3 algebra. We explicitly construct various T- and Q-operators which act in the irreducible highest weight modules of the W_3 algebra. These operators can be viewed as continuous field theory analogues of the commuting transfer matrices and Q-matrices of the integrable lattice systems associated with the quantum algebra U_q(\hat{sl}(3)). We formulate several conjectures detailing certain analytic characteristics of the Q-operators and propose exact asymptotic expansions of the T- and Q-operators at large values of the spectral parameter. We show, in particular, that the asymptotic expansion of the T-operators generates an infinite set of local integrals of motion of the W_3 CFT which in the classical limit reproduces an infinite set of conserved Hamiltonians associated with the classical Boussinesq equation. We further study the vacuum eigenvalues of the Q-operators (corresponding to the highest weight vector of the W_3 module) and show that they are simply related to the expectation values of the boundary exponential fields in the non-equilibrium boundary affine Toda field theory with zero bulk mass.Comment: LaTeX, 87 pages, 1 figure. Misprints correcte

Functional relations and nested Bethe ansatz for sl(3) chiral Potts model at q^2=-1

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl(3) chiral Potts model for q^2=-1. For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.Comment: 20 pages, 6 figures, to appear in J. Phys. A: Math. and Ge

Star-Triangle Relation for a Three Dimensional Model

The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice with two- and three-spin interactions. The corresponding local Boltzmann weights obey a number of simple relations, including a restricted star-triangle relation, which is a modified version of the well-known star-triangle relation appearing in two-dimensional models. We show that these relations lead to remarkable symmetry properties of the Boltzmann weight function of an elementary cube of the lattice, related to spatial symmetry group of the cubic lattice. These symmetry properties allow one to prove the commutativity of the row-to-row transfer matrices, bypassing the tetrahedron relation. The partition function per site for the infinite lattice is calculated exactly.Comment: 20 pages, plain TeX, 3 figures, SMS-079-92/MRR-020-92. (corrupted figures replaced

Transfer matrix eigenvectors of the Baxter-Bazhanov-Stroganov τ2\tau_2-model for N=2

We find a representation of the row-to-row transfer matrix of the Baxter-Bazhanov-Stroganov $\tau_2$-model for N=2 in terms of an integral over two commuting sets of grassmann variables. Using this representation, we explicitly calculate transfer matrix eigenvectors and normalize them. It is also shown how form factors of the model can be expressed in terms of determinants and inverses of certain Toeplitz matrices.Comment: 23 page

Universal integrability objects

We discuss the main points of the quantum group approach in the theory of quantum integrable systems and illustrate them for the case of the quantum group $U_q(\mathcal L(\mathfrak{sl}_2))$. We give a complete set of the functional relations correcting inexactitudes of the previous considerations. A special attention is given to the connection of the representations used to construct the universal transfer operators and $Q$-operators.Comment: 21 pages, submitted to the Proceedings of the International Workshop "CQIS-2012" (Dubna, January 23-27, 2012

On Automorphisms and Universal R-Matrices at Roots of Unity

Invertible universal R-matrices of quantum Lie algebras do not exist at roots of unity. There exist however quotients for which intertwiners of tensor products of representations always exist, i.e. R-matrices exist in the representations. One of these quotients, which is finite dimensional, has a universal R-matrix. In this paper, we answer the following question: on which condition are the different quotients of U_q(sl(2)) (Hopf)-equivalent? In the case when they are equivalent, the universal R-matrix of one can be transformed into a universal R-matrix of the other. We prove that this happens only when q^4=1, and we explicitly give the expressions for the automorphisms and for the transformed universal R-matrices in this case.Comment: 11 pages, minor TeXnical revision to allow automatic TeXin

Quantum Sine(h)-Gordon Model and Classical Integrable Equations

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$with$p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the$Q$-function of the quantum sine-Gordon$(\alpha>0)$or sinh-Gordon$(\alpha<-1)$ models.Comment: 35 pages, 3 figure

Three-Dimensional Integrable Models and Associated Tangle Invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group, if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil

Eigenvectors of Baxter-Bazhanov-Stroganov \tau^{(2)}(t_q) model with fixed-spin boundary conditions

The aim of this contribution is to give the explicit formulas for the eigenvectors of the transfer-matrix of Baxter-Bazhanov-Stroganov (BBS) model (N-state spin model) with fixed-spin boundary conditions. These formulas are obtained by a limiting procedure from the formulas for the eigenvectors of periodic BBS model. The latter formulas were derived in the framework of the Sklyanin's method of separation of variables. In the case of fixed-spin boundaries the corresponding T-Q Baxter equations for the functions of separated variables are solved explicitly. As a particular case we obtain the eigenvectors of the Hamiltonian of Ising-like Z_N quantum chain model.Comment: 14 pages, paper submitted to Proceedings of the International Workshop "Classical and Quantum Integrable Systems" (Dubna, January, 2007