Taxonomy of Integrable and Ground-State Solvable Models: Jastrow Wavefunctions on Graphs and Parent Hamiltonians

• URL: http://arxiv.org/abs/2602.22315v1
• Date: Wed, 25 Feb 2026 19:00:02 GMT
• Title: Taxonomy of Integrable and Ground-State Solvable Models: Jastrow Wavefunctions on Graphs and Parent Hamiltonians
• Authors: Nilanjan Sasmal, Adolfo del Campo,
• Abstract summary: 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.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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