One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature

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Abstract
We compute exactly the one particle reduced density matrix ρ (r) of a system of impenetrable bosons in one dimension at zero temperature. We do this by relating ρ (r) to a certain double scaling limit of the transverse correlation function of the one‐dimensional spin 1/2 X–Y model. We study the asymptotic behavior of ρ (r) for large r. This expansion contains oscillatory terms which arise due to the intrinsic quantum mechanical nature of the problem. We use these results to discuss the analytic structure of the momentum density function n (k).