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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Ontology / Topics
See full Ontology or Topics database.Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 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]