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 $L\sim 8\times 10^3$.

arXiv comment12 pages, 17 figures, 2 tables. Minor corrections to Table I, Figure 4, and Equations (28) and (29). Conclusions unchanged

References in corpus (27)

• Simulated Tempering: A New Monte Carlo Scheme
• Simulating Lattice Gauge Theories within Quantum Technologies
• Critical slowing down and error analysis in lattice QCD simulations
• Lattice QCD without topology barriers
• Equivariant flow-based sampling for lattice gauge theory
• Theta dependence of SU(N) gauge theories
• Finite volume QCD at fixed topological charge
• QCD at Fixed Topology
• Critical slowing down of topological modes
• Hybrid Monte Carlo and topological modes of full QCD
• Topological vacuum structure of the Schwinger model with matrix product states
• The U_A(1) Problem on the Lattice with Ginsparg-Wilson Fermions
• Automatic differentiation for error analysis of Monte Carlo data
• Tensor network formulation of the massless Schwinger model
• Stochastic locality and master-field simulations of very large lattices
• Master-field simulations of O(a)-improved lattice QCD: Algorithms, stability and exactness
• Fighting topological freezing in the two-dimensional CP${}^{N-1}$ model
• Metadynamics Surfing on Topology Barriers: the $C{P}^{N-1}$ Case
• Topological susceptibility at $T>T_{\mathrm{c}}$ from master-field simulations of the SU(3) gauge theory
• Large-$N$ $SU(N)$ Yang-Mills theories with milder topological freezing
• Topological Zero Modes in Monte Carlo Simulations
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• Ergodic sampling of the topological charge using the density of states
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Topology on the lattice; 2d Yang-Mills theories with a theta term
• Studying and removing effects of fixed topology
• Topological effects in continuum 2d $U(N)$ gauge theories

Cited by in corpus (7)

• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions
• Flow-based sampling in the lattice Schwinger model at criticality
• 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