Correlation reconstruction in non-uniform one-dimensional systems: the example of the free Fermi gas (Prof. J. Dubail)

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 entanglement entropies in trapped one-dimensional gases.

We will also discuss a seemingly unrelated problem: the entanglement growth of local operators in Heisenberg picture, which plays a key role in understanding the efficiency/non-efficiency of Heisenberg-picture DMRG. We will shed light on one of the early observations of Prosen and Pizorn [Phys. Rev. A 76, 032316, 2007]: that the entanglement of operators carrying a Jordan-Wigner string grows logarithmically in time.