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

Massimo Ostilli·Carlo Presilla
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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.

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Massimo Ostilli, Carlo Presilla. 2004-11-16. Ground state of many-body lattice systems: an analytical probabilistic approach. https://doi.org/10.1088/1367-2630%2F6%2F1%2F107

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