A perturbative probabilistic approach to quantum many-body systems

TL;DR

This paper introduces a perturbative probabilistic method for quantum many-body systems that maintains a multinomial structure while incorporating correlations, effectively addressing the phase problem in Hubbard models.

Contribution

A novel perturbative expansion of the probability distribution that preserves uncorrelated structure and includes correlations, improving analysis of quantum many-body systems.

Findings

Successfully tested on spin 1/2 hard-core boson Hubbard models

Handles phase problems caused by magnetic fields

Maintains multinomial structure at all perturbation orders

Abstract

In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the potential and hopping (amplitude and phase) values recorded during an infinitely lengthy evolution. We introduce a perturbative expansion of this probability distribution which conserves, at any order, a multinomial-like structure, typical of uncorrelated systems, but includes, order by order, the statistical correlations provided by the cumulant expansion. The proposed perturbative scheme is successfully tested in the case of pseudo spin 1/2 hard-core boson Hubbard models also when affected by a phase problem due to an applied magnetic field.