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Title: 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 imple- mented 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 demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electronmore » 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.« less

Authors:
 [1];  [1];  [1]
  1. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1148859
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review B; Journal Volume: 90; Journal Issue: 3
Country of Publication:
United States
Language:
English
Subject:
quantum monte carlo; energy density; density matrix

Citation Formats

Krogel, Jaron T, Kim, Jeongnim, and Reboredo, Fernando A. Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study. United States: N. p., 2014. Web. doi:10.1103/PhysRevB.90.035125.
Krogel, Jaron T, Kim, Jeongnim, & Reboredo, Fernando A. Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study. United States. doi:10.1103/PhysRevB.90.035125.
Krogel, Jaron T, Kim, Jeongnim, and Reboredo, Fernando A. Wed . "Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study". United States. doi:10.1103/PhysRevB.90.035125.
@article{osti_1148859,
title = {Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study},
author = {Krogel, Jaron T and Kim, Jeongnim and Reboredo, Fernando A},
abstractNote = {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 imple- mented 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 demonstrates a quantita- tive 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.},
doi = {10.1103/PhysRevB.90.035125},
journal = {Physical Review B},
number = 3,
volume = 90,
place = {United States},
year = {Wed Jan 01 00:00:00 EST 2014},
month = {Wed Jan 01 00:00:00 EST 2014}
}