Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study

Abstract

We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques implemented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences shows a quantitative connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.

9 pages, 5 figures

References in corpus (6)

• Continuum variational and diffusion quantum Monte Carlo calculations
• Applications of quantum Monte Carlo methods in condensed systems
• System-size convergence of point defect properties: The case of the silicon vacancy
• Diffusion quantum Monte Carlo calculation of the quasiparticle effective mass of the two-dimensional homogeneous electron gas
• Quasiparticle Effective Mass for the Two- and Three-Dimensional Electron Gas
• The Quantum Energy Density: Improved Efficiency for Quantum Monte Carlo

Cited by in corpus (3)

• Molecular-Atomic Transition in the Deuterium Hugoniot with Coupled Electron Ion Monte Carlo
• Introducing screening in one-body density matrix functionals: impact on the Extended Koopmans' Theorem's charged excitations of model systems
• Screened extended Koopmans' theorem: photoemission at weak and strong correlation