arXiv subjects
Publications and source records attributed to Gianluca Fuwa.
We present an algorithm that addresses topological freezing in lattice QCD simulations by combining parallel tempering with collective-variable-based enhanced sampling methods, and apply it to a particularly challenging system with $N_f = 2$ staggered fermions. We find that the algorithm unfreezes the system, which is otherwise completely frozen for approximately 40000 Molecular Dynamics Units with the Rational Hybrid Monte Carlo algorithm.
We present numerical results of staggered fermions with a taste splitting mass term on dynamical configurations. The rise of gluonic counterterms from rotational symmetry breaking is studied for a single taste operator and the pion propagator is computed. Preliminary numerical results are given for lattice sizes up to 16^4.
We present a high-precision study of the topological susceptibility in $SU(3)$ pure gauge theory in four space-time dimensions. The result is based on ensembles at seven lattice spacings and in seven physical volumes to facilitate a controlled continuum and infinite-volume extrapolation. We use a gluonic topological charge measurement, with gradient flow smoothing in the operator. Two complementary smoothing strategies are used (one keeps the flow time fixed in lattice units, one in physical units). Our data support the idea that both strategies yield a universal continuum limit; we find $χ_\mathrm{top}^{1/4}r_0=0.4775(14)(11)$ or $χ_\mathrm{top}^{1/4}=198.1(0.7)(2.7)\,\mathrm{MeV}$. Our appendix data suggest that the excess kurtosis $\langle q^4 \rangle / \langle q^2 \rangle^2-3$ decreases $\propto L^{-2}$ for large box sizes $L$.
In theories with topological sectors, such as lattice QCD and four-dimensional SU(N) gauge theories with periodic boundary conditions, conventional update algorithms suffer from topological freezing due to large action barriers separating distinct sectors. With appropriately constructed bias potentials, Metadynamics and related enhanced sampling techniques can mitigate this problem and significantly reduce the integrated autocorrelation times of the topological charge and associated observables. We test strategies to accelerate the buildup of bias potentials and the possibility of extrapolating potentials from small to large volumes. We also investigate the effectiveness of orthogonal algorithmic improvements, such as longer HMC trajectories and HMC variants, which may benefit conventional simulations as well.
When approaching the continuum limit in lattice QCD or other theories in a setup with topological sectors, conventional update algorithms experience a particularly severe form of critical slowing down that is caused by high action barriers between the sectors. The qualitative scaling behavior of this critical slowing down appears to be universal across different update algorithms and (gauge) actions. We demonstrate that a combination of Metadynamics with parallel tempering, along with other modifications, can significantly reduce autocorrelation times while avoiding the need for reweighting. We also discuss strategies to extend the methods to QCD simulations with dynamical fermions, and present first results for $N_f = 2$ simulations at unphysical pion masses.
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.