Extended Data Fig. 7: QMC finite-size scaling and extrapolation to the thermodynamic limit. | Nature Physics

Extended Data Fig. 7: QMC finite-size scaling and extrapolation to the thermodynamic limit.

From: Quantum phase diagram of high-pressure hydrogen

Extended Data Fig. 7

KZK-corrected lattice-regularized DMC energies for 4 crystalline symmetries (C2/c-24, Cmca-12, Cmca-4, and Cs-IV) plotted as a function of 1/N, where N is the number of atoms in the supercell, with respect to their value at N = 96, taken as reference. The energies are twisted-averaged in the canonical ensemble over a k-grid that has been rescaled according to the size of the supercell, as explained in SI. Note that despite the KZK correction and the canonical k-average, there is a residual size dependence beyond N = 96, larger than the target accuracy of ± 1 meV per atom, that needs to be extrapolated. As expected, this residual dependence is stronger in the atomic metallic phase and in the molecular phases under higher pressure, where the metallic character is enhanced.

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