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Bulletin of the American Physical Society

First principle calculations of long range correlation effects within the random phase approximation

Deyu Lu, Yan Li, Hugh F. Wilson, Giulia Galli

Published Mar 16, 2009• 0 citations
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We present a new method to obtain interaction part of a model Hamiltonian from the result of the first-principles calculation. The effective interaction contained in the model is determined based on the random phase approximation (RPA). In contrast to previous methods such as projected RPA or constrained RPA, the new method takes into account the long-range part of the polarization effect when determining the interaction in the model. After we discuss problems in previous RPA methods, we will give the formulation of the new method, and show how it works for the single-band Hubbard model of HgBa2_22​CuO4_44​.
We present an embedding approach to treat local electron correlation effects in periodic environments. In a single consistent framework, our plane wave based scheme embeds a local high-level correlation calculation [here, Coupled Cluster (CC) theory], employing localized orbitals, into a low-level correlation calculation [here, the direct Random Phase Approximation (RPA)]. This choice allows for an accurate and efficient treatment of long-range dispersion effects. Accelerated convergence with respect to the local fragment size can be observed if the low-level and high-level long-range dispersions are quantitatively similar, as is the case for CC in RPA. To demonstrate the capabilities of the introduced embedding approach, we calculate adsorption energies of molecules on a surface and in a chabazite crystal cage, as well as the formation energy of a lattice impurity in a solid at the level of highly accurate many-electron perturbation theories. The absorption energy of a methane molecule in a zeolite chabazite is converged with an error well below 20 meV at the CC level. As our largest periodic benchmark system, we apply our scheme to the adsorption of a water molecule on titania in a supercell containing more than 1000 electrons.
We have applied the model-mapped random phase approximation (RPA) [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and HgBa2CuO4{\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}HgBa2​CuO4​, resulting in two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results explain relative height of Tc{T}_{c}Tc​ observed in experiment for La2CuO4{\mathrm{La}}_{2}{\mathrm{CuO}}_{4}La2​CuO4​ and HgBa2CuO4{\mathrm{HgBa}}_{2}{\mathrm{CuO}}_{4}HgBa2​CuO4​. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.