|
Recently tensor product approximation has made substantial progress in
highdimensional approximation.
Some recent tensor formats fit into the framework of tensor networks, like
the TT-format as welll as the hierarchical format. These techniques allow
to approximate wavefunctions in the fermionic Fock space as tensor
≅ &otimesi=1k R2
with a storage requirement formally scaling linearly in k.
In this representation the formalism of second quantization could be used
numerically.
The Schrödinger equations leads to a tensor optimization problem
with additional constraints
given in terms the particle number operator. With increasing tensor
ranks this solution
can approximate the full CI wave function up to any required precision.
We present a local optimzation calculus numerical for solving
optimization problems in these tensor formats.
|
