Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many

Abstract

We show that the contact parameter of N harmonically-trapped interacting 1D bosons at zero temperature can be analytically and accurately obtained by a simple rescaling of the exact two-boson solution, and that N-body effects can be almost factorized. The small deviations observed between our analytical results and DMRG calculations are more pronounced when the interaction energy is maximal (i.e. at intermediate interaction strengths) but they remain bounded by the large-N local-density approximation obtained from the Lieb-Liniger equation of state stemming from the Bethe Ansatz. The rescaled two-body solution is so close to the exact ones, that is possible, within a simple expression interpolating the rescaled two-boson result to the local-density, to obtain N-boson contact and ground state energy functions in very good agreement with DMRG calculations. Our results suggest a change of paradigm in the study of interacting quantum systems, giving to the contact parameter a more fundamental role than energy.

7 pages, 4 figures. Revised version

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Cited by in corpus (9)

• Breakdown of Tan's relation in lossy one-dimensional Bose gases
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Universal off-diagonal long-range order behaviour for a trapped Tonks-Girardeau gas
• Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Momentum correlations of a few ultra-cold bosons escaping from an open well
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures