Theoretical analysis of multi-boson algorithm with local and global update of bosonic fields

TL;DR

This paper provides a theoretical cost analysis of the multi-boson algorithm with local and global updates, revealing its computational complexity and efficiency improvements in non-hermitian approximation.

Contribution

It offers a novel theoretical estimate of the multi-boson method's computational cost, including effects of local and global scalar field updates.

Findings

Cost scales as V(log V)^2/m^4 in non-hermitian approximation

Global updates reduce cost by a factor of m with a log V overhead

Provides insights into algorithm efficiency and scalability

Abstract

We estimate theoretically the cost of the multi-boson method in the non-hermitian approximation. It is shown that it is proportional to $V(\log V)^2/m^4$. For a global update of the scalar fields the cost decreases by a factor $m$ with a $\log V$ overhead.