Abstract

In spite of the tremendous successes of conformal field theory (CFT) in describing large-scale, universal, effects in one-dimensional (1D) systems at quantum critical points, their applicability has been limited to situations in which the bulk is uniform: CFT describes low-energy excitations around some energy scale, assumed to be constant throughout the system. However, in many experimental situations, quantum systems are strongly inhomogeneous: for instance, quantum gases in trapping potentials always have a non-uniform density; this is also true in many out-of-equilibrium situations, for instance when a gas is released from its trap. Here, we will argue that the powerful CFT approach can be adapted to deal with such 1D situations, relying on the example of lattice and continuous Fermi gases. The system’s inhomogeneity enters the field theory action through parameters that vary with position; in particular, the metric itself varies, resulting in a CFT in curved space. As an illustration, new exact formulas for entanglement entropies—-that have recently become experimentally measurable, and that are usually very difficult to calculate—-will be derived.