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 $\alpha$. 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 $\alpha$ 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 $Q$-functions, the solutions of Baxter's $t$-$Q$-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 XXZXXZ-chain at finite temperatures

We evaluate numerically certain multiple integrals representing nearest and next-nearest neighbor correlation functions of the spin-1/2 $XXZ$ 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 $\gamma$ 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 $\Delta>1$, extending our previous results to the full parameter plane of the antiferromagnetic chain ($\Delta > -1$ and arbitrary field $h$). The factorized formulae are numerically efficient and allow for taking the isotropic limit ($\Delta = 1$) and the Ising limit ($\Delta = \infty$). 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 $\Delta$ 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