Decimation map in 2D for accelerating HMC

To accelerate the HMC with field transformation, we consider a variant of the trivializing map, the decimation map, which can be regarded as a coarse-graining transformation. Using the 2D $U(1)$ pure gauge model, combined with the guided Monte Carlo algorithm, we show that the integrated autocorrelation time of the topological charge can be exponentially improved in the wall clock time. Our study indicates that incorporating renormalization group picture is a powerful and essential ingredient to accelerate the HMC at large $\beta$.