Truncated Calogero-Sutherland models

Abstract

A one-dimensional quantum many-body system consisting of particles confined in a harmonic potential and subject to finite-range two-body and three-body inverse-square interactions is introduced. The range of the interactions is set by truncation beyond a number of neighbors and can be tuned to interpolate between the Calogero-Sutherland model and a system with nearest and next-nearest neighbors interactions discussed by Jain and Khare. The model also includes the Tonks-Girardeau gas describing impenetrable bosons as well as a novel extension with truncated interactions. While the ground state wavefunction takes a truncated Bijl-Jastrow form, collective modes of the system are found in terms of multivariable symmetric polynomials. We numerically compute the density profile, one-body reduced density matrix, and momentum distribution of the ground state as a function of the range $r$ and the interaction strength.

arXiv comment10 pages, 10 figures, Revised section 2 and 3, Added Appendix, Phys. Rev. B (TBP 2017)

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• One-dimensional mixtures of several ultracold atoms: a review
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• Rationally extended many-body truncated Calogero-Sutherland model
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Truncated Calogero-Sutherland Models on a Circle
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
• Local Hamiltonians for one-dimensional critical models
• Parent Hamiltonians of Jastrow Wavefunctions