Matrix Product State representation for Slater Determinants and Configuration Interaction States

Slater determinants are product states of filled quantum fermionic orbitals. When they are expressed in a configuration space basis chosen a priori, their entanglement is bound and controlled. This suggests that an exact representation of Slater determinants as finitely-correlated states is possible. In this paper we analyze this issue and provide an exact Matrix Product representation for Slater determinant states. We also argue possible meaningful extensions that embed more complex configuration interaction states into the description.