[Paper Review] Dynamical overlap fermions with increased topological tunnelling

Nigel Cundy, Stefan Krieg+2 more|arXiv (Cornell University)|Oct 9, 2007

Quantum Chromodynamics and Particle Interactions12 references4 citations

TL;DR

This paper improves the dynamical overlap HMC algorithm by introducing a stable eigenvector differentiation method for the fermionic force and by exactly simulating part of the fermion determinant, which increases topological tunnelling rates by over tenfold and significantly reduces auto-correlation in lattice QCD simulations.

ABSTRACT

We present two improvements to our previous dynamical overlap HMC algorithm. We introduce a new method of differentiating the eigenvectors of the Kernel operator, which removes an instability in the fermionic force. Secondly, by simulating part of the fermion determinant exactly, without pseudo-fermions, we are able to increase the rate of topological tunnelling by a factor of more than ten, reducing the auto-correlation.

Motivation & Objective

• To address instability in the fermionic force calculation within the dynamical overlap HMC algorithm.
• To reduce auto-correlation in lattice QCD simulations caused by slow topological tunnelling.
• To increase the rate of topological tunnelling by accurately simulating a portion of the fermion determinant without relying on pseudo-fermions.
• To improve the efficiency and reliability of dynamical overlap fermion simulations for lattice gauge theory.

Proposed method

• A new method for differentiating the eigenvectors of the Kernel operator is introduced to stabilize the fermionic force calculation.
• A portion of the fermion determinant is simulated exactly, bypassing the need for pseudo-fermions in that part of the calculation.
• The exact determinant simulation enhances topological tunnelling by reducing the effective barrier between topological sectors.
• The improved force stability and enhanced tunnelling are integrated into the existing dynamical overlap HMC framework.
• The method maintains the exact chiral symmetry of the overlap fermion action while improving algorithmic performance.
• The algorithm is validated through numerical simulations showing reduced auto-correlation and faster topological sampling.

Experimental results

Research questions

• RQ1 How can the instability in the fermionic force arising from eigenvector differentiation be resolved in dynamical overlap fermion simulations?
• RQ2 To what extent can exact simulation of part of the fermion determinant improve topological tunnelling in HMC algorithms?
• RQ3 What is the quantitative impact of the new method on auto-correlation times in dynamical overlap simulations?
• RQ4 Can the combination of stable force calculation and enhanced tunnelling lead to more efficient sampling of topological sectors?

Key findings

• The new eigenvector differentiation method successfully eliminates instability in the fermionic force calculation.
• Topological tunnelling rates increase by a factor of more than ten compared to the previous algorithm.
• Auto-correlation times are significantly reduced due to the enhanced rate of topological tunnelling.
• The exact simulation of part of the fermion determinant improves the accuracy and stability of the HMC dynamics.
• The method maintains the exact chiral symmetry of the overlap fermion action while improving algorithmic efficiency.
• The overall performance of dynamical overlap fermion simulations is substantially enhanced through reduced correlation and faster sampling of topological sectors.