Correlation matrix renormalization approximation for total energy calculations of correlated electron systems

The recently introduced correlation matrix renormalization approximation (CMRA) was further developed by adopting a completely factorizable form for the renormalization z-factors, which assumes the validity of the Wick's theorem with respect to Gutzwiller wave function. This approximation (CMR-II) shows better dissociation behavior than the original one (CMR-I) based on the straightforward generalization of the Gutzwiller approximation to two-body interactions. We further improved the performance of CMRA by redefining the z-factors as a function of f(z) in CMR-II, which we call CMR-III. We obtained an analytical expression of f(z) by enforcing the equality in energy functional between CMR-III and full configuration interaction for the benchmark minimal basis H2. We show that CMR-III yields quite good binding energies and dissociation behaviors for various hydrogen clusters with converged basis set. Finally, we apply CMR-III to hydrogen crystal phases and compare the results with quantum Monte Carlo.