SciPost Submission Page
Parent Hamiltonians of Jastrow Wavefunctions
by Mathieu Beau, Adolfo del Campo
Submission summary
| As Contributors: | Mathieu Beau |
| Preprint link: | scipost_202107_00025v1 |
| Date submitted: | 2021-07-14 13:36 |
| Submitted by: | Beau, Mathieu |
| Submitted to: | SciPost Physics |
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.