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

Dubail, Jerome; Stéphan, Jean-Marie; Viti, Jacopo; Calabrese, Pasquale

doi:10.21468/SciPostPhys.2.1.002

SciPost Physics

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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.2.1.002
TI  - Conformal field theory for inhomogeneous one-dimensional quantum  systems: the example of non-interacting Fermi gases
PY  - 2017/02/13
UR  - https://www.scipost.org/SciPostPhys.2.1.002
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 2
IS  - 1
SP  - 002
A1  - Dubail, Jerome
AU  - Stéphan, Jean-Marie
AU  - Viti, Jacopo
AU  - Calabrese, Pasquale
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.2.1.002,
	title={{Conformal field theory for inhomogeneous one-dimensional quantum  systems: the example of non-interacting Fermi gases}},
	author={Jérôme Dubail and Jean-Marie Stéphan and Jacopo Viti and Pasquale Calabrese},
	journal={SciPost Phys.},
	volume={2},
	pages={002},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.2.1.002},
	url={https://scipost.org/10.21468/SciPostPhys.2.1.002},
}

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Ontology / Topics

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Conformal field theory (CFT) Conformal field theory (CFT) in curved spaces Entanglement entropy Free fermions Out-of-equilibrium systems Quantum criticality Quantum gases Spatially inhomogeneous systems

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