Local embedding/downfolding auxiliary-field quantum Monte Carlo (AFQMC)

A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method (Shiwei Zhang and Henry Krakauer, Phys. Rev. Lett. 90, 136401 (2003)). Local embedding in the occupied space (Yudis Virgus, Wirawan Purwanto, Henry Krakauer, and Shiwei Zhang, Phys. Rev. Lett. 113, 175502 (2014)) and local effective downfolding in the virtual space are employed to treat strongly correlated local clusters with an effective Hamiltonian. The accuracy is controlled by two geometric cutoff parameters that define the occupied space embedding and virtual downfolding regions. The systematic cutoff dependence of relative energies of physical and chemical interest is found to converge rapidly to the full AFQMC treatment. Thus, significant computational savings is achieved while maintaining a high degree of accuracy. This significantly increases the system size which can be accurately treated with AFQMC. Applications to transition metal atoms in 1D and in graphitic environments are presented. (Shiwei Zhang also acknowledges the Center for Computational Quantum Physics, Flatiron Institute).