  At fine lattice spacings, Markov chain Monte Carlo simulations of QCD and
other gauge theories with or without fermions are plagued by slow modes that
give rise to large autocorrelation times. This can lead to simulation runs that
are effectively stuck in one topological sector, a problem known as topological
freezing. Here, we demonstrate that for a relevant set of parameters,
Metadynamics can be used to unfreeze 4-dimensional SU(3) gauge theory. However,
compared to local update algorithms and the Hybrid Monte Carlo algorithm, the
computational overhead is significant in pure gauge theory, and the required
reweighting procedure may considerably reduce the effective sample size. To
deal with the latter problem, we propose modifications to the Metadynamics bias
potential and the combination of Metadynamics with parallel tempering. We test
the new algorithm in 4-dimensional SU(3) gauge theory and find that it can
achieve topological unfreezing without compromising the effective sample size,
thereby reducing the autocorrelation times of topological observables by at
least two orders of magnitude compared to conventional update algorithms.
Additionally, we observe significantly improved scaling of autocorrelation
times with the lattice spacing in 2-dimensional U(1) gauge theory.
