Metropolis sampling is perhaps the most well-known classical Monte Carlo method to study thermodynamic properties of materials. However, the temperature dependence of the resulting Boltzmann distribution makes it inefficient for studying complex systems, as simulations need to be repeated at different temperatures. Multicanonical algorithms such as Wang-Landau sampling [1] alleviate this problem by sampling the temperature independent density of energy states, or the energy degeneracy, from which thermodynamic properties at any temperature can be calculated at a later stage. This makes multicanonical methods more desirable for combining with first-principles methods like Density Functional Theory to carry out ab initio Monte Carlo simulations. To perform these simulations efficiently on high performance computers, two algorithms are proposed recently: one is a parallel framework for Wang-Landau sampling, namely Replica-Exchange Wang-Landau sampling [2], for invoking an additional level of parallelism that utilizes multiple Monte Carlo walkers. Another one is a histogram-free multicanonical method [3], for obtaining a basis expansion of the density of states and to reduce the number of Monte Carlo steps required to converge the simulations by approximately one order of magnitude. We will demonstrate how these novel algorithms are able to decrease the simulation time, and how they enable first-principles based Monte Carlo simulations for the prediction of materials properties to high accuracy.
[1] F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001).
[2] T. Vogel, Y. W. Li, T. Wuest, and D. P. Landau, Phys. Rev. Lett. 110, 210603 (2013).
[3] Y. W. Li and M. Eisenbach, in Proceedings of the Platform for Advanced Scientific Computing Conference (PASC '17). Association for Computing Machinery (ACM), New York, NY, USA, Article 10, 7 pages (2017).
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