Relativistic reduced density matrix functional theory

TL;DR

This paper extends reduced density matrix functional theory to the relativistic domain using the no-pair approximation, introducing theoretical foundations and relativistic functional approximations for electron correlation effects.

Contribution

It develops a relativistic RDMFT framework with the no-pair approximation and proposes relativistic versions of existing RDMFT functionals.

Findings

Theoretical extension of RDMFT to relativistic systems.

Introduction of relativistic RDMFT functionals.

Discussion of properties of relativistic functional approximations.

Abstract

As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the first-order reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties