Higher Order Auxiliary Field Quantum Monte Carlo Methods

TL;DR

This paper introduces higher order auxiliary field quantum Monte Carlo methods that improve the efficiency and accuracy of simulations for strongly correlated electron systems by developing new complex-hermitian splitting techniques.

Contribution

It presents novel higher order splitting methods for AFQMC based on the Hubbard-Stratonovich transformation, enhancing the method's precision and efficiency.

Findings

New complex-hermitian splitting methods demonstrated

Higher order methods outperform second order in efficiency

Comparative analysis shows improved accuracy over existing methods

Abstract

The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (https://alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.