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.
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