Lattice QCD without topology barriers

TL;DR

This paper introduces a method using open boundary conditions in lattice QCD to prevent topological charge trapping, enabling more accurate simulations as the continuum limit is approached.

Contribution

It proposes and validates a boundary condition modification that allows topological charge flow, reducing simulation bias in lattice QCD.

Findings

Open boundary conditions eliminate topological barriers.

Autocorrelation times scale with the inverse square of lattice spacing.

HMC algorithm aligns with Langevin universality class.

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.