Quantum Monte Carlo calculations in solids with downfolded Hamiltonians

Abstract

We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to dial, in principle, between the simplest model and the original Hamiltonian. As a by-product, pseudopotential errors are essentially eliminated using a frozen-core treatment. The computational cost of the many-body calculation is dramatically reduced without sacrificing accuracy. We use the auxiliary-field quantum Monte Carlo (AFQMC) method to solve the downfolded Hamiltonian. Excellent accuracy is achieved for a range of solids, including semiconductors, ionic insulators, and metals. We further test the method by determining the spin gap in NiO, a challenging prototypical material with strong electron correlation effects. This approach greatly extends the reach of general, ab initio many-body calculations in materials.

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• Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo
• Equation of state of warm-dense boron nitride combining computation, modeling, and experiment
• Hamiltonian symmetries in auxiliary-field quantum Monte Carlo calculations for electronic structure
• Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations
• Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo
• Investigation of the effective interactions for the Emery model by the constrained random-phase approximation and constrained functional renormalization group
• Ground state properties of one-dimensional and two-dimensional Hubbard model from Gutzwiller conjugate gradient minimization theory