Lattice QCD without topology barriers

Abstract

As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.

Plain TeX source, 26 pages, 4 figures included

References in corpus (5)

• Properties and uses of the Wilson flow in lattice QCD
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Critical slowing down and error analysis in lattice QCD simulations
• The Schrödinger functional in lattice QCD with exact chiral symmetry
• Non-renormalizability of the HMC algorithm

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