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

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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Cited by in corpus (5)

• Exact ground state for a class of matrix Hamiltonian models: quantum phase transition and universality in the thermodynamic limit
• Exact Monte Carlo time dynamics in many-body lattice quantum systems
• Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion
• Ground state of many-body lattice systems via a central limit theorem
• A perturbative probabilistic approach to quantum many-body systems