NON RELATIVISTIC QUANTUM FIELD THEORY: DYNAMICS AND IRREVERSIBILITY

We study aspects of quantum field theory at finite density using techniques and concepts from quantum information theory. We focus on massive Dirac fermions with chemical potential in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. This c-function is not monotonous, and incorporates the long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next compute the Renyi entropies numerically, and find Friedel-type oscillations. Next, we analyze the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion developed by Cardy, we show how the mutual information detects the Fermi surface correlations already at leading order in the expansion. Finally, we analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge. We find that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy.