Finite temperature correlations in the Lieb-Liniger 1D Bose gas

We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional strongly-correlated system: the integrable 1D Bose gas with repulsive \delta-function interaction (Lieb-Liniger model). Focusing on the observable dynamical density-density function, we present a Bethe Ansatz-based method allowing for its accurate evaluation over a broad range of momenta, frequencies, temperatures and interaction parameters, in finite but large systems. We show how thermal fluctuations smoothen the zero temperature critical behavior and present explicit quantitative results in experimentally accessible regimes.Comment: 5 page

A Perron theorem for matrices with negative entries and applications to Coxeter groups

Handelman (J. Operator Theory, 1981) proved that if the spectral radius of a matrix $A$ is a simple root of the characteristic polynomial and is strictly greater than the modulus of any other root, then $A$ is conjugate to a matrix $Z$ some power of which is positive. In this article, we provide an explicit conjugate matrix $Z$, and prove that the spectral radius of $A$ is a simple and dominant eigenvalue of $A$ if and only if $Z$ is eventually positive. For $n\times n$ real matrices with each row-sum equal to $1$, this criterion can be declined into checking that each entry of some power is strictly larger than the average of the entries of the same column minus $\frac{1}{n}$. We apply the criterion to elements of irreducible infinite nonaffine Coxeter groups to provide evidences for the dominance of the spectral radius, which is still unknown.Comment: 14 page

How to calculate correlation functions of Heisenberg chains

We describe a method for calculating dynamical spin-spin correlation functions in the finite isotropic and anisotropic antiferromagnetic Heisenberg models. Our method is able to produce results with high accuracy over the full parameter space.Comment: Proceedings of the "Tenth Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors", Salerno, Oct 200