Accelerating the Hybrid Monte Carlo algorithm with ILU preconditioning

Mike Peardon

Home/Archive/arXiv

arXiv · hep-lat/0011080

Accelerating the Hybrid Monte Carlo algorithm with ILU preconditioning

Mike Peardon

View original source ↗Read source document ↗Export metadata ↓

Abstract

The pseudofermion action of the Hybrid Monte Carlo (HMC) algorithm for dynamical fermions is modified to directly incorporate Incomplete LU (ILU) factorisation. This reduces the stochastic noise and allows a larger molecular dynamics step-size to be taken, cutting the computational cost. Numerical tests using the two-flavour Schwinger model are presented, where a two-step ILU preconditioning of the even-odd fermion matrix allows the step-size to be increased by a factor of two over the standard even-odd formulation.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Mike Peardon. 2000-12-12. Accelerating the Hybrid Monte Carlo algorithm with ILU preconditioning. https://arxiv.org/abs/hep-lat/0011080

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

When the center matters: color screening and gluelumps in dihedral lattice gauge theories

Confinement is one of the hallmarks of quantum chromodynamics (QCD), but its first-principles characterization remains elusive. We show that discrete non-Abelian lattice gauge theories (LGTs) with dihedral groups $D_N$ provide a minimal setup for characterizing the connection between confinement and the group center. When the latter is trivial (odd $N$), gluon clouds screen static charges, forming composite objects known as gluelumps. These are stable excitations of the theory, in contrast to their QCD analog. As a consequence, string breaking can occur through fluctuations of the electric field only, without pair nucleation from the vacuum. Our results showcase how the rich physics typically associated with QCD emerges in much simpler discrete non-Abelian LGTs, making them ideal settings to test this phenomenology both in numerical calculations and in near-term quantum devices.

hep-lat↗

arXiv2026

Confining Flux Tube in the Trace Deformed (2+1) Dimensional SU(2) Gauge Theory

We study the confining flux tube in the reconfined phase of trace deformed SU(2) Yang-Mills theory in (2+1) dimensions. Using lattice simulations above the standard deconfinement temperature, we analyze Polyakov-loop correlators and extract the ground state energy of the effective string. We show that the usual Nambu-Goto effective string description, including its standard higher-order corrections, fails to reproduce the data as the trace deformation is increased. Remarkably, deep in the reconfined regime the results are instead accurately described by the Polchinski-Yang rigid-string solution, corresponding to an effective string dominated by an extrinsic-curvature term. We further investigate the transverse profile of the chromo-electric flux tube and find significant deviations from the standard Yang-Mills behavior, including a substantial modification of the intrinsic width. Finally, we present an exploratory study of the phase diagram, finding evidence for a transition from a continuous to a first order reconfinement line as the deformation parameter increases. These results suggest that the reconfined phase realizes a qualitatively different effective-string regime from ordinary confinement.

hep-lat↗

arXiv2026

Quantum anomaly for benchmarking quantum computing

Given the rapid advances in quantum computing hardware, establishing strategies for verifying the correctness of quantum computations has become increasingly important. Exploiting the fact that the axial anomaly in gauge theories is exact to all orders in perturbation theory, we propose the axial anomaly as a nontrivial benchmark for quantum simulations of lattice gauge theories. We simulate axial charge production in ${\mathbb Z}_N$ lattice gauge theories on the trapped-ion quantum computer ``Reimei''. After taking the U(1), infinitesimal time, and infinite volume limits, we successfully reproduce the anomaly coefficient within statistical uncertainties, even without error mitigation. Our results demonstrate that the axial anomaly can be simulated on current quantum computers and serves as a verification test of quantum computations.

hep-lat↗