Approximation schemes for the study of multi-band Gutzwiller wave functions

TL;DR

This paper investigates approximation methods for multi-band Gutzwiller wave functions, highlighting the accuracy of diagonal ansatz in high-symmetry cases and proposing schemes for complex, lower-symmetry situations.

Contribution

It introduces approximation schemes for multi-band Gutzwiller energy minimization, especially useful when full minimization is computationally demanding.

Findings

Diagonal Ansatz is accurate in high-symmetry cases

Discrepancies increase with lower symmetry due to crystal-field and spin-orbit effects

Proposes approximate schemes for complex multi-band scenarios

Abstract

The minimum of the Gutzwiller energy functional depends on the number of parameters considered in the variational state. For a three-orbital Hubbard model we find that the frequently used diagonal Ansatz is very accurate in high-symmetry situations. For lower symmetry, induced by a crystal-field splitting or the spin-orbit coupling, the discrepancies in energy between the most general and a diagonal Gutzwiller Ansatz can be quite significant. We discuss approximate schemes that may be employed in multi-band cases where a minimization of the general Gutzwiller energy functional is too demanding numerically.