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

2004/07/31 by Massimo Ostilli, Carlo Presilla · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Spectral Theory in Mathematical Physics #cond-mat.other #hep-lat #math-ph #math.MP #math.PR #quant-ph

paper · pdf · doi:10.1088/1367-2630/6/1/107

published as New J.Phys. 6 (2004) 107

openalex publication_date 2004/08/13 · arxiv created 2004/11/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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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• A perturbative probabilistic approach to quantum many-body systems

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