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| Format: | Preprint |
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2026
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| Online-Zugang: | https://arxiv.org/abs/2602.22315 |
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| _version_ | 1866911469450297344 |
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| author | Sasmal, Nilanjan del Campo, Adolfo |
| author_facet | Sasmal, Nilanjan del Campo, Adolfo |
| contents | We introduce a family of many-body systems of distinguishable continuous-variable particles in which interparticle interactions are set by the adjacency matrix of a graph. The ground-state wavefunction of such systems is of a generalized Jastrow form involving the product of pair-correlation functions over the edge set of the graph. These systems describe quantum fluids when the graph is complete, and the pair function has a well-defined permutation symmetry. In general, they provide the continuous-variable generalization of spin systems on graphs, with broken permutation symmetry. The corresponding parent Hamiltonian is shown to include (a) two-body interactions determined by the graph adjacency matrix and (b) three-body interactions over all possible 2-paths on the graph. Employing elements of graph theory, we chart the landscape of models, recovering known instances in the literature and providing numerous new examples of ground-state solvable models for which the system Hamiltonian, ground-state wavefunction, and corresponding energy eigenvalue are specified. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22315 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Taxonomy of Integrable and Ground-State Solvable Models: Jastrow Wavefunctions on Graphs and Parent Hamiltonians Sasmal, Nilanjan del Campo, Adolfo Quantum Physics Quantum Gases Mathematical Physics We introduce a family of many-body systems of distinguishable continuous-variable particles in which interparticle interactions are set by the adjacency matrix of a graph. The ground-state wavefunction of such systems is of a generalized Jastrow form involving the product of pair-correlation functions over the edge set of the graph. These systems describe quantum fluids when the graph is complete, and the pair function has a well-defined permutation symmetry. In general, they provide the continuous-variable generalization of spin systems on graphs, with broken permutation symmetry. The corresponding parent Hamiltonian is shown to include (a) two-body interactions determined by the graph adjacency matrix and (b) three-body interactions over all possible 2-paths on the graph. Employing elements of graph theory, we chart the landscape of models, recovering known instances in the literature and providing numerous new examples of ground-state solvable models for which the system Hamiltonian, ground-state wavefunction, and corresponding energy eigenvalue are specified. |
| title | Taxonomy of Integrable and Ground-State Solvable Models: Jastrow Wavefunctions on Graphs and Parent Hamiltonians |
| topic | Quantum Physics Quantum Gases Mathematical Physics |
| url | https://arxiv.org/abs/2602.22315 |