81 research outputs found
Properties of linear integral equations related to the six-vertex model with disorder parameter
One of the key steps in recent work on the correlation functions of the XXZ
chain was to regularize the underlying six-vertex model by a disorder parameter
. For the regularized model it was shown that all static correlation
functions are polynomials in only two functions. It was further shown that
these two functions can be written as contour integrals involving the solutions
of a certain type of linear and non-linear integral equations. The linear
integral equations depend parametrically on and generalize linear
integral equations known from the study of the bulk thermodynamic properties of
the model. In this note we consider the generalized dressed charge and a
generalized magnetization density. We express the generalized dressed charge as
a linear combination of two quotients of -functions, the solutions of
Baxter's --equation. With this result we give a new proof of a lemma on
the asymptotics of the generalized magnetization density as a function of the
spectral parameter.Comment: 10 pages, latex, needs ws-procs9x6.cls, dedicated to Prof. Tetsuji
Miwa on the occasion of his 60th birthday; v2 minor correction
A note on the Bethe ansatz solution of the supersymmetric t-J model
The three different sets of Bethe ansatz equations describing the Bethe
ansatz solution of the supersymmetric t-J model are known to be equivalent.
Here we give a new, simplified proof of this fact which relies on the
properties of certain polynomials. We also show that the corresponding transfer
matrix eigenvalues agree.Comment: 6 pages, Latex, contributed to the 12th Int. Colloquium on Quantum
Groups and Integrable Systems, Prague, 200
Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic -chain at finite temperatures
We evaluate numerically certain multiple integrals representing nearest and
next-nearest neighbor correlation functions of the spin-1/2 Heisenberg
infinite chain at finite temperatures.Comment: 22 pages, 6 figure
Bethe Ansatz
The term Bethe Ansatz stands for a multitude of methods in the theory of
integrable models in statistical mechanics and quantum field theory that were
designed to study the spectra, the thermodynamic properties and the correlation
functions of these models non-perturbatively. This essay attempts to a give a
brief overview of some of these methods and their development, mostly based on
the example of the Heisenberg model and the corresponding six-vertex model.Comment: 28 pages, contribution to the 2nd edition of the Encyclopedia of
Mathematical Physic
Universal Low Temperature Asymptotics of the Correlation Functions of the Heisenberg Chain
We calculate the low temperature asymptotics of a function that
generates the temperature dependence of all static correlation functions of the
isotropic Heisenberg chain.Comment: Proceedings of the International Workshop "Recent Advances in Quantum
Integrable Systems" (Annecy, France
Short-distance thermal correlations in the massive XXZ chain
We explore short-distance static correlation functions in the infinite XXZ
chain using previously derived formulae which represent the correlation
functions in factorized form. We compute two-point functions ranging over 2, 3
and 4 lattice sites as functions of the temperature and the magnetic field in
the massive regime , extending our previous results to the full
parameter plane of the antiferromagnetic chain ( and arbitrary
field ). The factorized formulae are numerically efficient and allow for
taking the isotropic limit () and the Ising limit (). At the critical field separating the fully polarized phase from the
N\'eel phase, the Ising chain possesses exponentially many ground states. The
residual entropy is lifted by quantum fluctuations for large but finite
inducing unexpected crossover phenomena in the correlations.Comment: 24 pages, color onlin
Integral representation of the density matrix of the XXZ chain at finite temperatures
We present an integral formula for the density matrix of a finite segment of
the infinitely long spin-1/2 XXZ chain. This formula is valid for any
temperature and any longitudinal magnetic field.Comment: 12 pages, Late
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