Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases

• Main Author: Jérôme Dubail, Jean-Marie Stéphan, Jacopo Viti, Pasquale Calabrese
• Format: Article
• Language: English
• Published: SciPost 2017-02-01
• Series: SciPost Physics
• Online Access: https://scipost.org/SciPostPhys.2.1.002

Conformal field theory (CFT) has been extremely successful in describing large-scale universal effects in one-dimensional (1D) systems at quantum critical points. Unfortunately, its applicability in condensed matter physics has been limited to situations in which the bulk is uniform because CFT describes low-energy excitations around some energy scale, taken to be constant throughout the system. However, in many experimental contexts, such as quantum gases in trapping potentials and in several out-of-equilibrium situations, systems are strongly inhomogeneous. We show here that the powerful CFT methods can be extended to deal with such 1D situations, providing a few concrete examples for non-interacting 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. This approach allows us to derive exact formulas for entanglement entropies which were not known by other means.