One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable

Abstract

The exchange operator formalism (EOF) describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by EOF and the complete infinite family of parent Hamiltonians (PHJ) describing quantum many-body models with ground-states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the PHJ family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension. We give a variety of examples exemplifying the integrability of Hamiltonians in this family.

5+15 pages, no figures. More examples as well as a general user-guide to construct PHJ family of integrable models are included

References in corpus (5)

• Physics and Mathematics of Calogero particles
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Anyon-fermion mapping and applications to ultracold gases in tight waveguides
• Exactly-solvable system of one-dimensional trapped bosons with short and long-range interactions

Cited by in corpus (5)

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• Generalized Calogero-Sutherland models for Kondo physics in the Luttinger liquid