Analytical probabilistic approach to the ground state of lattice quantum systems: exact results in terms of a cumulant expansion

TL;DR

This paper introduces an analytical probabilistic method using cumulant expansions to exactly determine ground-state energies and correlations in lattice quantum systems, enabling analytical insights into their properties.

Contribution

It develops a cumulant-based series expansion approach for ground-state analysis, providing exact results and potential for analytical solutions in lattice quantum models.

Findings

Exact series expansion for ground-state energy and correlations

Analytical expressions as functions of Hamiltonian parameters

Potential applications in quantum system analysis

Abstract

We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state, are exactly determined as a series expansion in the cumulants of the multiplicities of the potential and hopping energies assumed by the system during its long-time evolution. Once these cumulants are known, even at a finite order, our approach provides the ground state analytically as a function of the Hamiltonian parameters. A scenario of possible applications of this analyticity property is discussed.