Fully ergodic simulations using radial updates

A sensible application of the hybrid Monte Carlo (HMC) method is often hindered by the presence of large—or even infinite—potential barriers. These potential barriers separate the configuration space into distinct sectors and can lead to ergodicity violations that bias measurements. In this work, we address this problem by augmenting HMC with a multiplicative Metropolis-Hastings update in a “radial direction” of the fields which enables crossing the potential barriers and ensures ergodicity of the sampling algorithm at comparably low computational cost. We demonstrate the algorithm on a simple toy model and show how it can be applied to the fermionic Hubbard model describing physics ranging from an exactly solvable two-site system to the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msub><a:mi mathvariant="normal">C</a:mi><a:mn>20</a:mn></a:msub><a:msub><a:mi mathvariant="normal">H</a:mi><a:mn>12</a:mn></a:msub></a:mrow></a:math> perylene molecule. Our numerical results show that the radial updates successfully remove ergodicity violations, while simultaneously reducing autocorrelation times.