Ground state of many-electron systems based on the action function

Abstract

The Hilbert space for an interacting electron system increases exponentially with electron number $N$. This limits the concept of wavefunctions $\psi$ based on solutions of the Schr\"odinger equation to $N \leq N_0$ with $N_0 \simeq 10^3$ \cite{Kohn1999}. It is argued that this exponential wall problem (EWP) is connected with an increasing redundance of information contained, e.g., in the ground-state of the system and it's wavefunction. The EWP as well as redundance of information are avoided when the characterization of the ground state is based on the action function $R$ rather than on the solutions $\psi$ of the Sch\"odinger equation. Both are related through a logarithm, i.e., $R = -i \hbar \ ln \psi$. Working with the logarithm is made possible by the use of cumulants. It is pointed out the way electronic structure calculations for periodic solids may use this concept.