# Local embedding and effective downfolding in the auxiliary-field quantum Monte Carlo method

## TL;DR

This paper introduces a local embedding and downfolding scheme in AFQMC that reduces computational costs by focusing on a local cluster and effectively downfolding virtual orbitals, enabling larger system simulations.

## Contribution

The methodology extends local embedding in AFQMC to include virtual orbital downfolding, significantly reducing computational effort while maintaining accuracy.

## Key findings

- AFQMC energies converge rapidly with respect to active region sizes.
- The approach allows treatment of larger systems with reduced computational resources.
- Systematic dependence on active region sizes is characterized.

## Abstract

A local embedding and effective downfolding scheme has been developed and implemented in the auxiliary-field quantum Monte Carlo (AFQMC) method. A local cluster in which electrons are fully correlated is defined and the frozen orbital method is used on the remainder of the system to construct an effective Hamiltonian which operates within the local cluster. Local embedding, which involves only the occupied sector, has previously been employed in the context of Co/graphene. Here, the methodology is extended in order to allow for effective downfolding of the virtual sector thus allowing for significant reduction in the computational effort required for AFQMC calculations. The system size which can be feasibly treated with AFQMC is therefore greatly extended as only a single local cluster is explicitly correlated at the AFQMC level of theory. The approximation is controlled by the separate choice of the spatial size of the active occupied region, $R_o$, and of the active virtual region, $R_v$. The systematic dependence of the AFQMC energy on $R_o$ and $R_v$ is investigated and it is found that relative AFQMC energies of physical and chemical interest converge rapidly to the full AFQMC treatment (i.e. using no embedding or downfolding).