A second-quantized red herring in full configuration-interaction Monte Carlo

TL;DR

This paper examines the sign problem in full configuration-interaction quantum Monte Carlo, clarifying conditions under which second quantization affects the sign problem, with corrections to previous claims and a comprehensive analysis.

Contribution

It provides a corrected, detailed discussion of when the sign problem differs between first and second quantization for various Hamiltonians.

Findings

Conditions for sign problem differences clarified

Corrected previous claims about second quantization effects

Comprehensive analysis of Hamiltonian basis dependence

Abstract

This paper deals with the sign problem in full configuration-interaction quantum Monte Carlo. After putting this article on the arxiv, it was pointed out to us that our argument applies to a number of model Hamiltonians we considered numerically but not to the most generic case. Please see arxiv: 1209.3044, where we have a corrected comprehensive discussion of the necessary and sufficient conditions for when the sign problem for a given Hamiltonian (and basis) differ between first and second quantization.