Electronic structure calculations at finite temperature using the piecewise interaction picture density matrix quantum Monte Carlo approach

In this work, we present a modification to the propagator in density matrix quantum Monte Carlo methods (DMQMC) which is a method to sample the N-body density matrix for an electronic Hamiltonian. Starting from the interaction picture (IP) requires IP-DMQMC to sample only one temperature during a single calculation; this was developed to alleviate the under-sampling of the important energy states. The new approach combines the IP-DMQMC and DMQMC propagators in a piecewise fashion (PIP-DMQMC) allowing for near-continuous temperature sampling. We benchmark this method by comparing to the sum over full configuration interaction (FCI) states, IP-DMQMC, and DMQMC. We find equivalent or improved energy estimates for the benchmark systems. We then use initiator PIP-DMQMC to simulate the water and methane molecules in the cc-pVDZ basis. Finally, we compare the cost of this method to that of the original IP-DMQMC method. We believe this method will extend the size of systems which can be accurately treated with finite temperature and will provide useful comparison data for other finite temperature methods.