Correlation functions of harmonic lattices in d-dimensional space

Abstract We study the correlation functions between the dynamical variables and between their conjugate momenta at sites of a harmonic lattice in the d-dimensional Euclidean space. We show that at the thermodynamic limit, they can be expressed in terms of Lauricella’s C-type hypergeometric functions. Furthermore, using these expressions, we explicitly demonstrate that the correlators near the center of the lattice satisfying Dirichlet boundary conditions coincide with those for the lattice with the periodic boundary conditions. By utilizing these expressions, we expect to make it easier to create programs that compute fast and highly precise for the quantum information quantities of subsystems within lattices.