Jérôme Dubail, JeanMarie Stéphan, Jacopo Viti, Pasquale Calabrese
SciPost Phys. 2, 002 (2017) ·
published 13 February 2017

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Conformal field theory (CFT) has been extremely successful in describing
largescale universal effects in onedimensional (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 lowenergy 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 outofequilibrium 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 noninteracting 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.