Block Heat-Bath Proposals for Topology Sampling in the Schwinger Model

Hybrid Monte Carlo (HMC) freezes the topological charge of lattice gauge theories toward the continuum. In two dimensions the topological charge is the total magnetic flux in units of 2π, and the flux through a block of plaquettes is fixed by its boundary only modulo 2π. In flux variables the gauge field inside a b × b block can be redrawn exactly from its pure-gauge conditional distribution, with the fermions included by a Metropolis step on the determinant. Every update can change the topological charge without crossing an action barrier. Exact sampling thus replaces learning for the pure-gauge proposal; to our knowledge this is the first topology-changing block update for dynamical fermions built from an exact pure-gauge conditional proposal. The probability of changing the topology follows a pure-gauge formula and depends essentially only on s² ≃ b²/β. Over β = 2–16 the autocorrelation time of the topological charge falls on a single curve in s², with a minimum of about half a sweep, so the block size should grow as √β. Where pseudofermion HMC is frozen, the block update decorrelates the topology within a sweep and is 38 to 76 times more efficient than winding HMC with exact determinant ratios. It also reproduces the η′ correlator, which is distorted at fixed topology. Finally, a single unfactorized pseudofermion estimate of the determinant ratio loses one to two orders of magnitude of acceptance on local winding moves.