Taxonomy of integrable and ground-state solvable models: Jastrow wave functions on graphs and parent Hamiltonians

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 wave function 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 wave function, and corresponding energy eigenvalue are specified.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph)

arXiv:2602.22315 [quant-ph]

(or arXiv:2602.22315v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.22315 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. B 113, 235151 (2026)

https://doi.org/10.1103/g7hk-tlq1 Focus to learn more DOI(s) linking to related resources

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