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arXiv · 2401.05248

Improved Dirichlet boundary conditions for lattice gauge-fermion theories

Tobias Rindlisbacher·Kari Rummukainen·Ahmed Salami
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Abstract

Hybrid Monte Carlo (HMC) simulations of lattice gauge theories with fermionic matter rely on the invertibility of the lattice Dirac operator. Near-zero modes of the latter can therefore significantly slow down the update algorithm and cause instabilities. This is in particular a problem when dealing with massless fermions. Homogeneous temporal Dirichlet boundary conditions can be used to remove zero modes from massless lattice Dirac operators, but the standard implementation of these boundary conditions can cause severe finite-volume cutoff effects in regions of parameter space where the physics at the ultraviolet (UV) cutoff scale is dominated by the fermionic instead of the gauge action. In lattice quantum chromodynamics (QCD) this is usually not an issue, as the gauge action dominates the UV physics and the problem does not show up. In studies of beyond standard model (BSM) theories, on the other hand, the finite-volume artifacts can be severe. We have identified the origin of these IR cutoff effects and propose a simple improvement on the homogeneous temporal Dirichlet boundary conditions to prevent them. We demonstrate the benefits of using our improved boundary conditions at the example of SU(2) lattice gauge theory with $N_f=24$ massless Wilson-clover flavors. Due to the large number of fermions in this theory, the boundary-related finite volume artifacts are particularly strong, and the effect from switching from the normal to our improved homogeneous Dirichlet boundary conditions is therefore distinct.

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Tobias Rindlisbacher, Kari Rummukainen, Ahmed Salami. 2024-01-10. Improved Dirichlet boundary conditions for lattice gauge-fermion theories. https://arxiv.org/abs/2401.05248

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