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

Jérôme Dubail, Jean-Marie Stéphan, Jacopo Viti, Pasquale Calabrese

SciPost Phys. 2, 002 (2017) · published 13 February 2017

- doi: 10.21468/SciPostPhys.2.1.002
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### Abstract

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.

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^{1 }^{2 }Jerome Dubail, -
^{1 }^{3 }^{4 }Jean-Marie Stéphan, -
^{5 }Jacopo Viti, -
^{6 }^{7 }Pasquale Calabrese

^{1}Centre National de la Recherche Scientifique / French National Centre for Scientific Research [CNRS]^{2}Université de Lorraine [Univ Lorraine]^{3}Claude Bernard University Lyon 1 [UCBL]^{4}Max Planck Digital Library [MPDL]^{5}Instituto Internacional de Fisica / International Institute of Physics^{6}Istituto Nazionale di Fisica Nucleare (presso la SISSA) / National Institute of Nuclear Physics (at SISSA) [INFN at SISSA]^{7}Istituto Nazionale di Fisica Nucleare Sezione di Bologna [INFN Bologna]