Title: Dealing with the exponential wall in electronic structure calculations,
Abstract: An alternative to Density Functional Theory are wavefunction based electronic
structure calculations for solids. In order to perform them the Exponential
Wall (EW) problem has to be resolved. It is caused by an exponential increase
of the number of configurations with increasing electron number N. There are
different routes one may follow. One is to characterize a many-electron
wavefunction by a vector in Liouville space with a cumulant metric rather than
in Hilbert space. This removes the EW problem. Another is to model the solid by
an {\it impurity} or {\it fragment} embedded in a {\it bath} which is treated
at a much lower level than the former. This is the case in Density Matrix
Embedding Theory (DMET) or Density Embedding Theory (DET). The latter are
closely related to a Schmidt decomposition of a system and to the determination
of the associated entanglement. We show here the connection between the two
approaches. It turns out that the DMET (or DET) has an identical active space
as a previously used Local Ansatz, based on a projection and partitioning
approach. Yet, the EW problem is resolved differently in the two cases. By
studying a $H_{10}$ ring these differences are analyzed with the help of the
method of increments.