One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

Brun, Yannis; Dubail, Jerome

doi:10.21468/SciPostPhys.2.2.012

SciPost Physics

One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

Yannis Brun, Jérôme Dubail

SciPost Phys. 2, 012 (2017) · published 4 April 2017

doi: 10.21468/SciPostPhys.2.2.012
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Abstract

The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.2.2.012
TI  - One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance
PY  - 2017/04/04
UR  - https://www.scipost.org/SciPostPhys.2.2.012
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 2
IS  - 2
SP  - 012
A1  - Brun, Yannis
AU  - Dubail, Jerome
AB  - The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.
ER  -

@Article{10.21468/SciPostPhys.2.2.012,
	title={{One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance}},
	author={Yannis Brun and Jérôme Dubail},
	journal={SciPost Phys.},
	volume={2},
	pages={012},
	year={2017},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.2.2.012},
	url={https://scipost.org/10.21468/SciPostPhys.2.2.012},
}

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Ontology / Topics

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Conformal field theory (CFT) in curved spaces One-particle density matrix Spatially inhomogeneous systems Tonks-Girardeau gas

Authors / Affiliations: mappings to Contributors and Organizations

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¹ ² Yannis Brun,
¹ ² Jerome Dubail