On the grounds of a Feynman–Kac-type formula for Hamiltonian lattice systems, we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem applies. As a remarkable result, we find that the ground-state energy as well as all the correlation functions in the ground state are determined semi-analytically by solving a simple scalar equation. Furthermore, explicit solutions of this equation are obtained in the noninteracting case.
Ground state of many-body lattice systems: an analytical probabilistic approach / Ostilli, M; Presilla, Carlo. - In: NEW JOURNAL OF PHYSICS. - ISSN 1367-2630. - 6:(2004), p. 107. [10.1088/1367-2630/6/1/107]
Ground state of many-body lattice systems: an analytical probabilistic approach
PRESILLA, Carlo
2004
Abstract
On the grounds of a Feynman–Kac-type formula for Hamiltonian lattice systems, we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem applies. As a remarkable result, we find that the ground-state energy as well as all the correlation functions in the ground state are determined semi-analytically by solving a simple scalar equation. Furthermore, explicit solutions of this equation are obtained in the noninteracting case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.