Hybrid Monte Carlo simulations of finite-temperature properties of solids.

Monte Carlo (MC) algorithms constitute one of the cornerstone numerical frameworks of modern statistical physics. In contrast to molecular or spin dynamics (MD or SD), MC techniques are free of the realistic relaxation time scales and are meant to offer better estimates of "quai-static" thermodynamic averages at equilibrium. However, popular MC algorithms lack of scalable parallelization strategy for systems with long-range interactions and cannot be readily used for ab intio structural relaxation. Hybrid Monte Carlo algorithm (HMC) offers a straightforward solution to this drawback by incorporating MD into the random trial state generator. Surprisingly, despite its popularity in computational lattice field theory, the applications of HMC in the context of structural and spin dynamics are hard to find. In this study, we present an open-source HMC code for ultra-large-scale effective Hamiltonian simualtions and an implementation of HMC algorithm within Abinit software suite. We then present computational benchmarks and reveal advantages of this algorithm.