Measuring the Topological Susceptibility in a Fixed Sector

Abstract

For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( < Q^2 > - < Q >^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models and in 2d Abelian gauge theory yield accurate results for chi_t, which confirm that the method is applicable. We also obtain promising results in 4d SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.

28 pages, LaTex, 13 figures, 3 tables, new results for 2d U(1) and 4d SU(2) gauge theory. Final version to be published in Phys. Rev. D

References in corpus (11)

• Finite volume QCD at fixed topological charge
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Topological susceptibility in two-flavor lattice QCD with exact chiral symmetry
• Topological Lattice Actions
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Extracting hadron masses from fixed topology simulations
• Topology density correlator on dynamical domain-wall ensembles with nearly frozen topological charge
• Comparison of different lattice definitions of the topological charge
• Spin chain simulations with a meron cluster algorithm
• Extracting Physics from Topologically Frozen Markov Chains
• Combining ordinary and topological finite volume effects for fixed topology simulations

Cited by in corpus (11)

• FLAG Review 2019
• FLAG Review 2021
• FLAG Review 2024
• Topological susceptibility of QCD with dynamical Möbius domain wall fermions
• Lattice QCD on Non-Orientable Manifolds
• Interpreting Numerical Measurements in Fixed Topological Sectors
• Topological Susceptibility from Slabs
• Topological Susceptibility of the 2d O(3) Model under Gradient Flow
• Topology in the 2d Heisenberg Model under Gradient Flow
• Homotopy data as part of the lattice field: A first study
• Computing the topological susceptibility from fixed topology QCD simulations