Parent Hamiltonians of Jastrow Wavefunctions
Abstract
We find the complete family of manybody quantum Hamiltonians with groundstate of Jastrow form involving the pairwise product of a pair function in an arbitrary spatial dimension. The parent Hamiltonian generally includes a twobody pairwise potential as well as a threebody potential. We thus generalize the CalogeroMarchioro construction for the threedimensional case to arbitrary spatial dimensions. The resulting family of models is further extended to include a onebody term representing an external potential, which gives rise to an additional longrange twobody interaction. Using this framework, we provide the generalization to an arbitrary spatial dimension of wellknown systems such as the CalogeroSutherland and CalogeroMoser models. We also introduce novel models, generalizing the McGuire manybody quantum bright soliton solution to higher dimensions and considering groundstates which involve e.g., polynomial, Gaussian, exponential, and hyperbolic pair functions. Finally, we show how the pair function can be reverseengineered to construct models with a given potential, such as a pairwise Yukawa potential, and to identify models governed exclusively by threebody interactions.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.02869
 Bibcode:
 2021arXiv210702869B
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 16 pages, new references, improved introduction and conclusion, typo in ref [62] fixed