Simple regularization scheme for multi-reference density functional theories
W. Satula, J. Dobaczewski
Date: December 6, 2014
- Extensions of single-reference (SR) energy-density-functionals (EDFs)
to multi-reference (MR) applications involve using the generalized
Wick theorem (GWT), which leads to singular energy kernels that
cannot be properly integrated to restore symmetries, unless the EDFs
are generated by true interactions.
- We propose a new method to regularize the MR EDFs, which is based on
using auxiliary quantities obtained by multiplying the kernels with
appropriate powers of overlaps.
- Regularized matrix elements of two-body interactions are obtained by
integrating the auxiliary quantities and then solving simple linear
- We implement the new regularization method within the self-consistent
Skyrme-Hartree-Fock approach and we perform a proof-of-principle
angular-momentum projection (AMP) of states in odd-odd nucleus
Al. We show that for EDFs generated by true
interactions, our regularization method gives results identical to
those obtained within the standard AMP procedure. We also show that
for EDFs that do not correspond to true interactions, it gives
stable and converging results that are different than unstable and
non-converging standard AMP values.
- The new regularization method proposed in this work may provide us
with a relatively inexpensive and efficient tool to generalize SR
EDFs to MR applications, thus allowing for symmetry restoration and
configuration mixing performed for typical nuclear EDFs, which most
often do not correspond to true interactions.