In this work we develop a new method piecewise interaction picture density matrix quantum Monte Carlo (PIP-DMQMC). PIP-DMQMC is based on the interaction picture density matrix quantum Monte Carlo method (IP-DMQMC). The DMQMC methods simulate the finite temperature electronic energy using the density matrix. Our method has two phases, in the first phase of a simulation we use the interaction picture propagator to calculate the density matrix at a specific inverse temperature, in the second phase we use the Schrödinger picture propagator to sample the density matrix at additional inverse temperatures. For a variety of test systems, we calculate the finite temperature electronic energy using PIP-DMQMC, DMQMC, IP-DMQMC and a sum over full CI states, making comparisons between all four methods. We find our development in general can achieve milli-Hartree accuracy and reduce stochastic noise all while sampling multiple temperatures in a single simulation. We then follow up with a brief investigation of the initiator approximation combined with PIP-DMQMC. To finish, we close with a discussion of the computational scaling for this method. We believe our method will expand milli-Hartree accurate finite temperature data in the literature, allowing others to make comparisons in the future.

Piecewise interaction picture density matrix quantum Monte Carlo: Reducing the cost of finite temperature electronic structure calculations

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