15,812 research outputs found
SU(N) Matrix Difference Equations and a Nested Bethe Ansatz
A system of SU(N)-matrix difference equations is solved by means of a nested
version of a generalized Bethe Ansatz, also called "off shell" Bethe Ansatz.
The highest weight property of the solutions is proved. (Part I of a series of
articles on the generalized nested Bethe Ansatz and difference equations.)Comment: 18 pages, LaTe
Bethe Ansatz for 1D interacting anyons
This article gives a pedagogic derivation of the Bethe Ansatz solution for 1D
interacting anyons. This includes a demonstration of the subtle role of the
anyonic phases in the Bethe Ansatz arising from the anyonic commutation
relations. The thermodynamic Bethe Ansatz equations defining the temperature
dependent properties of the model are also derived, from which some groundstate
properties are obtained.Comment: 22 pages, two references added, small improvements to tex
Exact solution of the simplest super-orthosymplectic invariant magnet
We present the exact solution of the invariant magnet by the Bethe
ansatz approach. The associated Bethe ansatz equation exhibit a new feature by
presenting an explicit and distinct phase behaviour in even and odd sectors of
the theory. The ground state, the low-lying excitations and the critical
properties are discussed by exploiting the Bethe ansatz solution.Comment: 8 pages, UFSCARF-TH-1
The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics
The asymmetric simple exclusion process (ASEP) plays the role of a paradigm
in non-equilibrium statistical mechanics. We review exact results for the ASEP
obtained by Bethe ansatz and put emphasis on the algebraic properties of this
model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP
are derived from the algebraic Bethe ansatz. Using these equations we explain
how to calculate the spectral gap of the model and how global spectral
properties such as the existence of multiplets can be predicted. An extension
of the Bethe ansatz leads to an analytic expression for the large deviation
function of the current in the ASEP that satisfies the Gallavotti-Cohen
relation. Finally, we describe some variants of the ASEP that are also solvable
by Bethe ansatz.
Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent
advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and
J. Feinberg editor
Algebraic Bethe ansatz for the gl(12) generalized model II: the three gradings
The algebraic Bethe ansatz can be performed rather abstractly for whole
classes of models sharing the same -matrix, the only prerequisite being the
existence of an appropriate pseudo vacuum state. Here we perform the algebraic
Bethe ansatz for all models with , rational, gl(12)-invariant
-matrix and all three possibilities of choosing the grading. Our Bethe
ansatz solution applies, for instance, to the supersymmetric t-J model, the
supersymmetric model and a number of interesting impurity models. It may be
extended to obtain the quantum transfer matrix spectrum for this class of
models. The properties of a specific model enter the Bethe ansatz solution
(i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz
equations) through the three pseudo vacuum eigenvalues of the diagonal elements
of the monodromy matrix which in this context are called the parameters of the
model.Comment: paragraph added in section 3, reference added, version to appear in
J.Phys.
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