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

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arxiv 1701.02248 v3 pith:TLLXMFAW submitted 2017-01-09 cond-mat.stat-mech cond-mat.quant-gasmath-phmath.MP

Yannis Brun , Jérôme Dubail This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.quant-gasmath-phmath.MP
keywords densityconformalmatrixone-dimensionalone-particlearbitraryasymptoticallybosons
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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.

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  1. Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials

    cond-mat.stat-mech 2025-05 conditional novelty 6.0 of 10

    For inhomogeneous free-boson chains, the leading entanglement entropy is (a*/6) log N, where a* is the scaling exponent of the region where the local potential vanishes.

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