10 research outputs found
Factorization of R-matrix and Baxter's Q-operator
The general rational solution of the Yang-Baxter equation with the symmetry
algebra sl(2) can be represented as the product of the simpler building blocks
denoted as R-operators. The R-operators are constructed explicitly and have
simple structure. Using the R-operators we construct the two-parametric
Baxter's Q-operator for the generic inhomogeneous periodic XXX spin chain. In
the case of homogeneous XXX spin chain it is possible to reduce the general
Q-operator to the much simpler one-parametric operator.Comment: 17 page
New Two-Dimensional Quantum Models Partially Solvable by Supersymmetrical Approach
New solutions for second-order intertwining relations in two-dimensional SUSY
QM are found via the repeated use of the first order supersymmetrical
transformations with intermediate constant unitary rotation. Potentials
obtained by this method - two-dimensional generalized P\"oschl-Teller
potentials - appear to be shape-invariant. The recently proposed method of
separation of variables is implemented to obtain a part of their
spectra, including the ground state. Explicit expressions for energy
eigenvalues and corresponding normalizable eigenfunctions are given in analytic
form. Intertwining relations of higher orders are discussed.Comment: 21 pages. Some typos corrected; imrovements added in Subsect.4.2;
some references adde
New Two-Dimensional Integrable Quantum Models from SUSY Intertwining
Supersymmetrical intertwining relations of second order in the derivatives
are investigated for the case of supercharges with deformed hyperbolic metric
. Several classes of particular solutions of these
relations are found. The corresponding Hamiltonians do not allow the
conventional separation of variables, but they commute with symmetry operators
of fourth order in momenta. For some of these models the specific SUSY
procedure of separation of variables is applied.Comment: 18 page
New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
The supersymmetric intertwining relations with second order supercharges
allow to investigate new two-dimensional model which is not amenable to
standard separation of variables. The corresponding potential being the
two-dimensional generalization of well known one-dimensional P\"oschl-Teller
model is proven to be exactly solvable for arbitrary integer value of parameter
all its bound state energy eigenvalues are found analytically, and the
algorithm for analytical calculation of all wave functions is given. The shape
invariance of the model and its integrability are of essential importance to
obtain these results.Comment: 23 page
Gustafson integrals
It was shown recently that many of the Gustafson integrals appear in studies of the spin chain models. One can hope to obtain a generalization of the Gustafson integrals considering spin chain models with a different symmetry group . In this paper we analyse the spin magnet with the symmetry group and derive several new integrals
Gustafson integrals for spin magnet
It was observed recently that multidimensional Mellin-Barnes integrals (Gustafson's integrals) arise naturally in studies of SL(2, R) spin chain models. We extend this analysis to noncompact SL(2, C) spin magnets and obtain an integral which generalizes Gustafson's integrals to the complex case