Ground state of many-body lattice systems: an analytical probabilistic approach
نویسنده
چکیده
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. PACS numbers: 02.50.-r, 05.40.-a, 71.10.Fd Ground state of many-body lattice systems: an analytical probabilistic approach 2
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