Finite temperature quantum embedding theories for correlated systems

TL;DR

This paper discusses the development of finite temperature quantum embedding theories, particularly self-energy embedding theory (SEET), which offers a controlled, accurate, and thermodynamically consistent approximation for solving the many-electron problem.

Contribution

It demonstrates that SEET is derivable from a universal functional, ensuring conservation laws, and shows how other methods like DMFT are special cases of SEET, enabling systematic convergence.

Findings

SEET is derived from a universal functional.

SEET satisfies conservation laws and thermodynamic consistency.

Other methods like DMFT are special cases of SEET.

Abstract

The cost of the exact solution of the many-electron problem is believed to be exponential in the number of degrees of freedom, necessitating approximations that are controlled and accurate but numerically tractable. In this paper, we show that one of these approximations, the self-energy embedding theory (SEET), is derivable from a universal functional and therefore implicitly satisfies conservation laws and thermodynamic consistency. We also show how other approximations, such as the dynamical mean field theory (DMFT) and its combinations with many-body perturbation theory, can be understood as a special case of SEET and discuss how the additional freedom present in SEET can be used to obtain systematic convergence of results.