Ground state of many-body lattice systems: an analytical probabilistic approach
Other Condensed Matter
2007-05-23 v2 High Energy Physics - Lattice
Mathematical Physics
math.MP
Probability
Quantum Physics
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.
Keywords
Cite
@article{arxiv.cond-mat/0407756,
title = {Ground state of many-body lattice systems: an analytical probabilistic approach},
author = {Massimo Ostilli and Carlo Presilla},
journal= {arXiv preprint arXiv:cond-mat/0407756},
year = {2007}
}