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.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.

quant-pharXiv:2602.22315Physical review. B./Physical review. BFeb 27, 20261 citation

Quantum graphs

Theoretical and mathematical physicsSep 22, 20080 citations

Cluster developments for Jastrow wave functions II Introduction of irreducible cluster functions

Chr.D. Hartogh, H.A. Tolhoek

PhysicaJan 1, 195816 citations

$N$ -representability of the Jastrow wave function pair density of the lowest-order$N$-representability of the Jastrow wave function pair density of the lowest-order

Katsuhiko Higuchi, Masahiko Higuchi

We have recently proposed a density functional scheme for calculating the ground-state pair density (PD) within the Jastrow wave function PDs of the lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A \textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the $N$ -representability of the LO-Jastrow PD. In this paper, the sufficient conditions for the $N$ -representability of the LO-Jastrow PD are derived. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.We have recently proposed a density functional scheme for calculating the ground-state pair density (PD) within the Jastrow wave function PDs of the lowest-order (LO-Jastrow PDs) [M. Higuchi and K. Higuchi, Phys. Rev. A \textbf{75}, 042510 (2007)]. However, there remained an arguable problem on the $N$-representability of the LO-Jastrow PD. In this paper, the sufficient conditions for the $N$-representability of the LO-Jastrow PD are derived. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.

arXiv:0801.0615Jan 4, 20080 citations

N

-representability of the Jastrow wave function pair density of the lowest-order

N

-representability of the LO-Jastrow PD. In this paper, the sufficient conditions for the

N

-representability of the LO-Jastrow PD are derived. These conditions are used as the constraints on the correlation function of the Jastrow wave function. A concrete procedure to search the suitable correlation function is also presented.