Path Integral Density Functional Theory

TL;DR

The paper introduces PI-DFT, a novel method combining path integrals and density functional theory to efficiently compute particle densities for many-electron systems without explicit wave functions, applicable to fermions and bosons.

Contribution

It presents a new computational approach that leverages path integrals within DFT, enabling efficient density calculations for many-particle quantum systems.

Findings

Numerical effort scales quadratically with particle number.

Applicable to both fermion and boson systems.

Provides a recursion formula for density calculations at different temperatures.

Abstract

A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly calculating individual wave functions. These densities can directly be used as an input to energy density functionals. Thus our method makes full use of the theorem of Hohenberg, Kohn and Sham which shows, that the energy of a many electron system only depends on the particle density. At glance we present a recursion formula for the calculation of many fermion and boson particle densities from one-particle densities at a set of different temperatures. For both statistics the numerical effort of our method increases only with the square of the particle number.