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Monte Carlo sampling of the canonical distribution presents a formidablechallenge when the potential energy landscape is characterized by a largenumber of local minima separated by high barriers. The principal observation ofthis work is that the multiple local minima and energy barriers in a landscapecan often occur as a result of discrete symmetries in the potential energyfunction. A new Monte Carlo method is proposed, group action Markov chain MonteCarlo (GA-MCMC), which augments more conventional trial moves (e.g. randomjumps, hybrid Monte Carlo, etc.) with the application of a group action from awell-chosen generating set of the discrete symmetry group; the result is aframework for symmetry-adapted MCMC. It is shown that conventional trial movesare generally optimal for "local mixing" rates, i.e. sampling a single energywell; whereas the group action portion of the GA-MCMC trial move allows theMarkov chain to propagate between energy wells and can vastly improve the rateof "global mixing". The proposed method is compared with standard jumps andumbrella sampling (a popular alternative for energy landscapes with barriers)for potential energies with translational, reflection, and rotationalsymmetries. GA-MCMC is shown to consistently outperform the consideredalternatives, even when the symmetry of the potential energy function isbroken. The work culminates by extending GA-MCMC to a clustering-type algorithmfor interacting dielectric polymer chains. Not only does GA-MCMC againoutperform the considered alternatives, but it is the only method whichconsistently converges for all of the cases considered. Some new andinteresting phenomena regarding the electro-elasticity of dielectric polymerchains, unveiled via GA-MCMC, is briefly discussed.

Group action Markov chain Monte Carlo for accelerated sampling of energy landscapes with discrete symmetries and energy barriers