Piecewise Interaction Picture Density Matrix Quantum Monte Carlo

TL;DR

This paper introduces a modified interaction picture density matrix quantum Monte Carlo method that efficiently samples a range of temperatures in a single run, reducing computational costs for simulating interacting electrons.

Contribution

The authors develop a piecewise approach combining interaction picture and Bloch equation techniques to improve temperature sampling efficiency in DMQMC methods.

Findings

Performance is comparable or superior to existing DMQMC methods.

Reduces computational cost by sampling multiple temperatures simultaneously.

Effective in molecular test systems.

Abstract

The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.