Topological sampling through windings

Abstract

We propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional $U(1)$ gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors$-$winding steps$-$combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the $U(1)$ pure gauge theory, which are known even at finite $\beta$. We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC$-$leading to significant deviations in topological as well as non-topological quantities$-$the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $L\sim 8\times 10^3$.

12 pages, 17 figures, 2 tables. Minor corrections to Table I, Figure 4, and Equations (28) and (29). Conclusions unchanged

References in corpus (7)

• Critical slowing down and error analysis in lattice QCD simulations
• Finite volume QCD at fixed topological charge
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Ergodic sampling of the topological charge using the density of states
• Studying and removing effects of fixed topology

Cited by in corpus (7)

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• Inhomogeneities in the $2$-Flavor Chiral Gross-Neveu Model
• On fits to correlated and auto-correlated data
• Simulating first-order phase transition with hierarchical autoregressive networks
• Memory efficient finite volume schemes with twisted boundary conditions
• Topological properties of minimally doubled fermions in two space-time dimensions