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

TL;DR

This paper demonstrates that one-dimensional quantum systems with ground-states of Jastrow form are integrable by establishing an equivalence with models described by the exchange operator formalism, including the long-range Lieb-Liniger model.

Contribution

It introduces a novel connection between the exchange operator formalism and the family of parent Hamiltonians with Jastrow ground-states, proving their integrability even with external potentials.

Findings

Established equivalence between EOF and PHJ models.

Proved integrability of the long-range Lieb-Liniger model.

Provided examples of integrable Hamiltonians in this family.

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.