Diagrammatic quantum field formalism for localized electrons

TL;DR

This paper introduces a diagrammatic quantum field formalism tailored for systems with localized electrons, enabling a convergent series expansion for energy calculations based on overlap integrals, applicable across various dimensions and spin configurations.

Contribution

The paper presents a novel diagrammatic formalism that simplifies and generalizes energy calculations for localized electron systems using a convergent overlap series expansion.

Findings

Effective for two-dimensional Wigner crystals

Applicable to spin-singlet states in low-density electron gases

Provides practical rules for arbitrary order overlap expansions

Abstract

We introduce a diagrammatic quantum field formalism for the evaluation of normalized expectation values of operators, and suitable for systems with localized electrons. It is used to develop a convergent series expansion for the energy in powers of overlap integrals of single-particle orbitals. This method gives intuitive and practical rules for writing down the expansion to arbitrary order of overlap, and can be applied to any spin configuration and to any dimension. Its applicability for systems with well localized electrons has been illustrated with examples, including the two-dimensional Wigner crystal and spin-singlets in the low-density electron gas.