17 research outputs found
Solutions of a discretized Toda field equation for from Analytic Bethe Ansatz
Commuting transfer matrices of vertex models obey the
functional relations which can be viewed as an type Toda field equation
on discrete space time. Based on analytic Bethe ansatz we present, for
, a new expression of its solution in terms of determinants and
Pfaffians.Comment: Latex, 14 pages, ioplppt.sty and iopl12.sty assume
From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model
We propose a nonlinear integral equation (NLIE) with only one unknown
function, which gives the free energy of the integrable one dimensional
Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum
Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives
the solution of the T-system, plays an important role. In addition, we also
calculate the high temperature expansion of the specific heat and the magnetic
susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added;
typos corrected; to appear in J. Phys. A: Math. Ge
Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras
We propose factorized difference operators L(u) associated with the twisted
quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}),
U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be
annihilated by a screening operator. Based on a basis of the solutions of the
difference equation L(u)w(u)=0, we also construct a Casorati determinant
solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page
Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model
We derive traditional thermodynamic Bethe ansatz (TBA) equations for the
sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer
matrix. These TBA equations are identical to the ones from the string
hypothesis. Next we derive a new family of nonlinear integral equations (NLIE).
In particular, a subset of these NLIE forms a system of NLIE which contains
only a finite number of unknown functions. For r=1, this subset of NLIE reduces
to Takahashi's NLIE for the XXX spin chain. A relation between the traditional
TBA equations and our new NLIE is clarified. Based on our new NLIE, we also
calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge