Jérôme DUBAIL (U. de Lorraine) : Conformal field theory of inhomogeneous one-dimensional quantum systems

Wednesday 9 Nov 2016, 15:00 → 17:00 Europe/Brussels

E/3rd floor-E.349 - Seminar room (E.349) (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

Abstract: Many large-scale, universal, effects in one-dimensional systems at quantum critical points can be tackled with a combination of methods from solvable lattice models and from field theory, usually conformal field theory (CFT) and Luttinger liquid ideas. Yet, the applicability of such tools in condensed matter physics is often limited to situations in which the bulk is uniform: CFT, in particular, describes low-energy excitations around some energy scale, assumed to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in many out-of-equilibrium situations, systems are strongly inhomogeneous. We will argue that standard CFT methods can nevertheless be extended to deal with such 1D situations, and we will illustrate the main idea with simple free fermion examples. The method we develop can be thought of as the Local Density Approximation (LDA) on steroids: while standard LDA allows to calculate density profiles (more generally, expectation values of local operators), here we use LDA to extract the position-dependent parameters that enter the field theory action, such as the components of the metric tensor. Then, once the action has been fixed, all correlation functions follow; this strategy will be illustrated with new results about correlation functions in trapped one-dimensional gases. We will also make connections with a seemingly unrelated problem in statistical physics: arctic circle phenomena in dimer coverings.