Accelerated histogram-free multicanonical Monte Carlo algorithm for the basis expansion of density of states*

We propose a novel Monte Carlo algorithm to obtain the density of states (DOS) in the form of a basis expansion, for physical systems with continuous state variables [1]. Our algorithm inherits the strengths of various previous methods such as multicanonical sampling and Wang-Landau sampling. Additionally, we advance the capability of these methods: Firstly, instead of a numerical array of finite resolutions, our algorithm obtains a basis set expansion for the DOS, with the number of terms and coefficients determined and refined iteratively during the simulation. Secondly, since the visited energies are stored directly in a data set instead of a histogram, this reduces the undesirable statistical noise and errors caused by the discretization of state observables. Thirdly, as the random walkers are directed to achieve uniform sampling of the phase space, our scheme is more efficient and we have demonstrated an order of magnitude of speedup compared to existing methods. We will show how this method is applied to accelerate the simulation of materials properties.
[1] Y. W. Li and M. Eisenbach, in Proceedings of PASC ’17, ACM, New York, NY, USA, Article 10 (2017).