453 research outputs found
Bethe ansatz for the three-layer Zamolodchikov model
This paper is a continuation of our previous work (solv-int/9903001). We
obtain two more functional relations for the eigenvalues of the transfer
matrices for the chiral Potts model at . This model, up to a
modification of boundary conditions, is equivalent to the three-layer
three-dimensional Zamolodchikov model. From these relations we derive the Bethe
ansatz equations.Comment: 22 pages, LaTeX, 5 figure
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
Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
Relation between the vacuum eigenvalues of CFT Q-operators and spectral
determinants of one-dimensional Schroedinger operator with homogeneous
potential, recently conjectured by Dorey and Tateo for special value of
Virasoro vacuum parameter p, is proven to hold, with suitable modification of
the Schroedinger operator, for all values of p.Comment: 9 pages, harvmac.tex, typos correcte
Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation
This paper is a direct continuation of\ \BLZ\ where we begun the study of the
integrable structures in Conformal Field Theory. We show here how to construct
the operators which act in highest weight Virasoro
module and commute for different values of the parameter . These
operators appear to be the CFT analogs of the - matrix of Baxter\ \Baxn, in
particular they satisfy famous Baxter's equation. We also
show that under natural assumptions about analytic properties of the operators
as the functions of the Baxter's relation allows
one to derive the nonlinear integral equations of Destri-de Vega (DDV)\ \dVega\
for the eigenvalues of the -operators. We then use the DDV equation to
obtain the asymptotic expansions of the - operators at large
; it is remarkable that unlike the expansions of the
operators of \ \BLZ, the asymptotic series for contains the
``dual'' nonlocal Integrals of Motion along with the local ones. We also
discuss an intriguing relation between the vacuum eigenvalues of the
- operators and the stationary transport properties in boundary sine-Gordon
model. On this basis we propose a number of new exact results about finite
voltage charge transport through the point contact in quantum Hall system.Comment: Revised version, 43 pages, harvmac.tex. Minor changes, references
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The vertex formulation of the Bazhanov-Baxter Model
In this paper we formulate an integrable model on the simple cubic lattice.
The -- valued spin variables of the model belong to edges of the lattice.
The Boltzmann weights of the model obey the vertex type Tetrahedron Equation.
In the thermodynamic limit our model is equivalent to the Bazhanov -- Baxter
Model. In the case when we reproduce the Korepanov's and Hietarinta's
solutions of the Tetrahedron equation as some special cases.Comment: 20 pages, LaTeX fil
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 . 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 -operators.Comment: 21 pages, submitted to the Proceedings of the International Workshop
"CQIS-2012" (Dubna, January 23-27, 2012
Quantization of the N=2 Supersymmetric KdV Hierarchy
We continue the study of the quantization of supersymmetric integrable KdV
hierarchies. We consider the N=2 KdV model based on the affine
algebra but with a new algebraic construction for the L-operator, different
from the standard Drinfeld-Sokolov reduction. We construct the quantum
monodromy matrix satisfying a special version of the reflection equation and
show that in the classical limit, this object gives the monodromy matrix of N=2
supersymmetric KdV system. We also show that at both the classical and the
quantum levels, the trace of the monodromy matrix (transfer matrix) is
invariant under two supersymmetry transformations and the zero mode of the
associated U(1) current.Comment: LaTeX2e, 12 page
Spectral zeta functions of a 1D Schr\"odinger problem
We study the spectral zeta functions associated to the radial Schr\"odinger
problem with potential V(x)=x^{2M}+alpha x^{M-1}+(lambda^2-1/4)/x^2. Using the
quantum Wronskian equation, we provide results such as closed-form evaluations
for some of the second zeta functions i.e. the sum over the inverse eigenvalues
squared. Also we discuss how our results can be used to derive relationships
and identities involving special functions, using a particular 5F_4
hypergeometric series as an example. Our work is then extended to a class of
related PT-symmetric eigenvalue problems. Using the fused quantum Wronskian we
give a simple method for calculating the related spectral zeta functions. This
method has a number of applications including the use of the ODE/IM
correspondence to compute the (vacuum) nonlocal integrals of motion G_n which
appear in an associated integrable quantum field theory.Comment: 15 pages, version
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