A Convergent Method for Calculating the Properties of Many Interacting Electrons

TL;DR

This paper introduces a convergent method using the projected density of transitions (PDoT) for calculating properties of many interacting electrons, enabling efficient and accurate analysis of extended systems.

Contribution

It presents a novel approach employing PDoT and continued fractions to compute electronic properties with exponential convergence, independent of system size.

Findings

Accurate calculation of binding energies and excitations in extended systems.

Demonstration on a spin-1/2 Heisenberg chain with comparison to analytic results.

Method exhibits exponential convergence, outperforming traditional numerical techniques.

Abstract

A method is presented for calculating binding energies and other properties of extended interacting systems using the projected density of transitions (PDoT) which is the probability distribution for transitions of different energies induced by a given localized operator, the operator on which the transitions are projected. It is shown that the transition contributing to the PDoT at each energy is the one which disturbs the system least, and so, by projecting on appropriate operators, the binding energies of equilibrium electronic states and the energies of their elementary excitations can be calculated. The PDoT may be expanded as a continued fraction by the recursion method, and as in other cases the continued fraction converges exponentially with the number of arithmetic operations, independent of the size of the system, in contrast to other numerical methods for which the number of operations increases with system size to maintain a given accuracy. These properties are illustrated with a calculation of the binding energies and zone-boundary spin- wave energies for an infinite spin-1/2 Heisenberg chain, which is compared with analytic results for this system and extrapolations from finite rings of spins.