Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions

TL;DR

This paper classifies all one-dimensional quantum potentials with near-neighbor interactions that have Jastrow-like ground states, revealing the necessity of three-body interactions and introducing new potential models.

Contribution

It provides a complete classification of such potentials and introduces new hyperbolic and elliptic models, expanding the understanding of ground states in quantum many-body systems.

Findings

All classified models include three-body interactions.

Introduces a new hyperbolic potential model.

Includes an elliptic interaction model reducing to known cases.

Abstract

We completely solve the problem of classifying all one-dimensional quantum potentials with nearest- and next-to-nearest-neighbors interactions whose ground state is Jastrow-like, i.e., of Jastrow type but depending only on differences of consecutive particles. In particular, we show that these models must necessarily contain a three-body interaction term, as was the case with all previously known examples. We discuss several particular instances of the general solution, including a new hyperbolic potential and a model with elliptic interactions which reduces to the known rational and trigonometric ones in appropriate limits.