The Quantum Energy Density: Improved Efficiency for Quantum Monte Carlo

TL;DR

This paper introduces a physically meaningful quantum energy density operator for Quantum Monte Carlo, enabling more efficient calculations of local energies and interfaces, with demonstrated accuracy on helium-neon gas and delta-doped silicon.

Contribution

The paper presents a new energy density operator for Quantum Monte Carlo that accurately represents local energies and simplifies calculations of interfaces and defects.

Findings

Energy density operator returns correct Hamiltonian when integrated.

Atomic energies match eigenvalues of isolated systems.

Interfacial energies can be computed more efficiently using the energy density.

Abstract

We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct Hamiltonian when integrated over a volume containing a cluster of particles. This property is demonstrated for a helium-neon "gas," showing that atomic energies obtained from the energy density correspond to eigenvalues of isolated systems. The formation energies of defects or interfaces are typically calculated as total energy differences. Using a model of delta-doped silicon (where dopant atoms form a thin plane) we show how interfacial energies can be calculated more efficiently with the energy density, since the region of interest is small. We also demonstrate how the energy density correctly transitions to the bulk limit away from the interface where the correct energy is obtainable from a separate total energy calculation.