20,364 research outputs found
Structure of Matrix Elements in Quantum Toda Chain
We consider the quantum Toda chain using the method of separation of
variables. We show that the matrix elements of operators in the model are
written in terms of finite number of ``deformed Abelian integrals''. The
properties of these integrals are discussed. We explain that these properties
are necessary in order to provide the correct number of independent operators.
The comparison with the classical theory is done.Comment: LaTeX, 17 page
Spin interfaces in the Ashkin-Teller model and SLE
We investigate the scaling properties of the spin interfaces in the
Ashkin-Teller model. These interfaces are a very simple instance of lattice
curves coexisting with a fluctuating degree of freedom, which renders the
analytical determination of their exponents very difficult. One of our main
findings is the construction of boundary conditions which ensure that the
interface still satisfies the Markov property in this case. Then, using a novel
technique based on the transfer matrix, we compute numerically the left-passage
probability, and our results confirm that the spin interface is described by an
SLE in the scaling limit. Moreover, at a particular point of the critical line,
we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex
model, which, in turn, relates to an integrable dilute Brauer model.Comment: 12 pages, 6 figure
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