Parent Hamiltonians of Jastrow Wavefunctions

• URL: http://arxiv.org/abs/2107.02869v3
• Date: Sun, 26 Sep 2021 11:41:43 GMT
• Title: Parent Hamiltonians of Jastrow Wavefunctions
• Authors: Mathieu Beau and Adolfo del Campo
• Abstract summary: We find the complete family of many-body quantum Hamiltonians with ground-state of Jastrow form. We generalize the Calogero-Marchioro construction for the three-dimensional case to arbitrary spatial dimensions. We show how the pair function can be reverse-engineered to construct models with a given potential.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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