[Paper Review] Theoretical analysis of multi-boson algorithm with local and global update of bosonic fields

Artan Boriçi|ArXiv.org|Feb 15, 1996

Advanced Photonic Communication Systems3 citations

TL;DR

This paper presents a theoretical analysis of the multi-boson algorithm for lattice field theory simulations, comparing local and global updates of bosonic fields. It derives that the computational cost scales as $V(\log V)^2/m^4$ for local updates, with a $m$-factor reduction and $\log V$ overhead when using global updates, offering a significant efficiency improvement for light fermions.

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.

Motivation & Objective

• To analyze the computational cost of the multi-boson algorithm in the non-Hermitian approximation.
• To compare the efficiency of local versus global updates for bosonic fields in lattice simulations.
• To determine the scaling behavior of the algorithm with respect to volume $V$ and fermion mass $m$.
• To evaluate the impact of global updates on reducing computational cost while accounting for additional overhead.

Proposed method

• Theoretical estimation of computational cost using non-Hermitian approximation in lattice field theory.
• Modeling the multi-boson algorithm with both local and global updates of scalar fields.
• Deriving asymptotic scaling behavior in terms of lattice volume $V$ and fermion mass $m$.
• Analyzing the trade-off between reduced cost and logarithmic overhead in global update schemes.
• Using asymptotic analysis to compare the $V(\log V)^2/m^4$ scaling for local updates with the modified scaling under global updates.
• Focusing on the cost of solving the fermion determinant via the multi-boson method in QCD-like models.

Experimental results

Research questions

• RQ1 What is the asymptotic computational cost of the multi-boson algorithm with local updates of bosonic fields?
• RQ2 How does the use of global updates affect the computational cost compared to local updates?
• RQ3 What is the scaling of the cost with respect to lattice volume $V$ and fermion mass $m$?
• RQ4 Does the global update scheme reduce cost despite introducing a $\log V$ overhead?
• RQ5 What is the theoretical efficiency gain of global over local updates in the multi-boson framework?

Key findings

• The computational cost of the multi-boson algorithm with local updates scales as $V(\log V)^2/m^4$.
• Global updates reduce the cost by a factor of $m$ compared to local updates.
• The global update method incurs a $\log V$ overhead in addition to the cost reduction.
• The $m$-factor reduction in cost is significant for light fermions, improving efficiency in simulations.
• The theoretical analysis confirms that global updates are more efficient despite the logarithmic overhead.
• The results are derived under the non-Hermitian approximation, relevant for lattice QCD with light quarks.