Response properties in phaseless auxiliary field quantum Monte Carlo

TL;DR

This paper introduces a method using automatic differentiation in phaseless AFQMC to efficiently compute response properties and reduced density matrices with minimal additional computational cost.

Contribution

The authors develop a novel approach applying automatic differentiation to phaseless AFQMC for response properties, maintaining energy calculation scaling and reducing computational overhead.

Findings

AD enables RDM calculations with similar scaling as energy computations

Cost prefactor for property calculations is less than four

Self-consistency and trial orbital choice impact property accuracy

Abstract

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo (AFQMC) through the application of automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices (RDMs) with the same computational cost scaling as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations.