Jérôme Dubail, Jean-Marie 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
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.
