Ground state of many-body lattice systems: an analytical probabilistic approach

Details Ground state of many-body lattice systems: an analytical probabilistic approach Ground state of many-body lattice systems: an analytical probabilistic approach

2004-07-29

arxiv.org/abs/cond-mat/0407756v2

New J.Phys. 6 (2004) 107

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1088/1367-2630/6/1/107

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.

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