arXiv subjects

Philip Rouenhoff

Publications and source records attributed to Philip Rouenhoff.

3 recordsLinked to original sources

arXiv2024

Topology in 2D non-Abelian Lattice Gauge Theories

In two dimensions, $U(N_c)$ gauge theories exhibit a non-trivial topological structure, while $SU(N_c)$ theories are topologically trivial. Hence, for $G = U(N_c)$ the phase space is divided into topological sectors, characterized by a topological index (a.k.a. ``topological charge''). These sectors are separated by action barriers, which diverge if the lattice spacing is taken small, resulting in an algorithmic problem known as ``topological freezing''. We study these theories in various box sizes and at various couplings. With the help of gradient flow we derive instanton-like solutions for 2D $U(N_c)$ theory with a specific focus on the case of $N_c = 2$.

hep-lat↗

arXiv2023

Topology changing update algorithms for SU(3) gauge theory

At fine lattice spacings, lattice simulations are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. We study the problem and possible algorithmic solutions in 4-dimensional SU(3) gauge theory, with special focus on instanton updates and Metadynamics.

hep-lat↗

arXiv2022

Metadynamics Surfing on Topology Barriers in the Schwinger Model

Topological freezing is a well known problem in lattice simulations: with shrinking lattice spacing a transition between topological sectors becomes increasingly improbable, leading to a problematic increase of the autocorrelation time regarding several observables. We present our investigation of metadynamics as a solution for topological freezing in the Schwinger model. Specifically, we take a closer look at the collective variable and its scaling behaviour, visualize the effects of topological freezing and how metadynamics helps in that respect and explore alternatives for a more efficient building process. Possible implications for and differences to four-dimensional SU(3) theory are briefly discussed.

hep-lat↗