Introducing fluctuation-driven order into density functional theory using the quantum order-by-disorder framework

Abstract

Density functional theory in the local or semi-local density approximation is a powerful tool for materials simulation, yet it struggles in many cases to describe collective electronic order that is driven by electronic interactions. In this work it is shown how arbitrary, fluctuation-driven electronic order may be introduced into density functional theory using the quantum order-bydisorder framework. This is a method of calculating the free energy correction due to collective spin and charge fluctuations about a state that hosts static order, in a self-consistent manner. In practical terms, the quantum order-by-disorder method is applied to the Kohn-Sham auxiliary system of density functional theory to give an order-dependent correction to the exchange-correlation functional. Calculation of fluctuation propagators within density functional theory renders the result fully first-principles. Two types of order are considered as examples -fluctuation-driven superconductivity and spin nematic order -and implementation schemes are presented in each case. CONTENTSIV. Introducing fluctuation-driven order into density functional theory 8 A. The interacting Kohn-Sham system 8 B. Superconductivity 9 C. Calculating fluctuation propagators within DFT 10 Retrofitting the QOBD-DFT result 11 Comparison to superconducting DFT 11 D. An implementation scheme for superconducting order 12 E. An implementation scheme for spin nematic order 13