Approximate formula for the macroscopic polarization including quantum fluctuations

TL;DR

This paper introduces an approximate formula for macroscopic polarization that incorporates quantum fluctuations, accurately capturing correlation effects and topological phenomena in complex many-body systems.

Contribution

It proposes a novel approximation using natural orbital geometric phases, improving the understanding of polarization and topological charge pumping in correlated materials.

Findings

Accurately reproduces polarization across insulator transitions

Predicts quenching of topological charge pumping due to interactions

Validates the approximation in the Rice-Mele-Hubbard model

Abstract

The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a one-body reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping.