Perturbative correction to the ground state properties of one-dimensional strongly interacting bosons in a harmonic trap

Abstract

We calculate the first-order perturbation correction to the ground state energy and chemical potential of a harmonically trapped boson gas with contact interactions about the infinite repulsion Tonks-Girardeau limit. With $c$ denoting the interaction strength, we find that for a large number of particles $N$ the $1/c$ correction to the ground state energy increases as $N^{5/2}$, in contrast to the unperturbed Tonks-Girardeau value that is proportional to $N^2$. We describe a thermodynamic scaling limit for the trapping frequency that yields an extensive ground state energy and reproduces the zero temperature thermodynamics obtained by a local density approximation.

arXiv comment5 pages, 3 PDF figures. Modifications to Fig. 1, experimental values. References added

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Cited by in corpus (6)

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• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Strongly interacting Bose-Fermi mixtures in one dimension
• Breakdown of the scale invariance in the vicinity of Tonks-Girardeau gas
• Strongly interacting one-dimensional bosons in arbitrary-strength optical lattices: from Bose-Hubbard to sine-Gordon and beyond
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases