Parent Hamiltonians of Jastrow Wavefunctions

TL;DR

This paper systematically constructs and extends many-body quantum Hamiltonians with Jastrow ground states across arbitrary dimensions, generalizing known models and introducing new ones with diverse interaction potentials.

Contribution

It provides a comprehensive framework for deriving parent Hamiltonians with Jastrow ground states in any dimension, including novel models and reverse-engineering methods for specific potentials.

Findings

Generalized Calogero-Marchioro models to arbitrary dimensions

Introduced new models with polynomial, Gaussian, exponential, and hyperbolic pair functions

Demonstrated how to construct models with specific potentials like Yukawa or pure three-body interactions

Abstract

We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a two-body pairwise potential as well as a three-body potential. We thus generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a one-body term representing an external potential, which gives rise to an additional long-range two-body interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of well-known systems such as the Calogero-Sutherland and Calogero-Moser models. We also introduce novel models, generalizing the McGuire many-body quantum bright soliton solution to higher dimensions and considering ground-states which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverse-engineered to construct models with a given potential, such as a pair-wise Yukawa potential, and to identify models governed exclusively by three-body interactions.