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.

Conformal field theory for inhomogeneous one-dimensional quantum systems: the example of non-interacting Fermi gases / Dubail, Jerome; Calabrese, Pasquale; Stéphan, Jean Marie; Viti, Jacopo. - In: SCIPOST PHYSICS. - ISSN 2542-4653. - 2:1(2017), pp. 1-21. [10.21468/SciPostPhys.2.1.002]

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

Calabrese, Pasquale;
2017

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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10.21468/SciPostPhys.2.1.002
https://arxiv.org/abs/1606.04401
Dubail, Jerome; Calabrese, Pasquale; Stéphan, Jean Marie; Viti, Jacopo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/48253
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