Gradientbased stochastic estimation of the density matrix
Fast estimation of the singleparticle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H) _{ij} decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. Here, we introduce a gradientbased probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zerotemperature metals, the stochastic error scales like S ^{(d+2)/2d}, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.
 Authors:

^{[1]};
^{[2]};
^{[3]}
;
^{[4]}
 Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy
 Univ. of Virginia, Charlottesville, VA (United States). Dept. of Physics
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Univ. of Tennessee, Knoxville, TN (United States). Dept. of Physics and Astronomy; Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Quantum Condensed Matter Division and ShullWollan Center
 Publication Date:
 Report Number(s):
 LAUR1730801
Journal ID: ISSN 00219606
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 148; Journal Issue: 9; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
 OSTI Identifier:
 1481135
 Alternate Identifier(s):
 OSTI ID: 1423724
Wang, Zhentao, Cher, GiaWei, Barros, Kipton Marcos, and Batista, Cristian D. Gradientbased stochastic estimation of the density matrix. United States: N. p.,
Web. doi:10.1063/1.5017741.
Wang, Zhentao, Cher, GiaWei, Barros, Kipton Marcos, & Batista, Cristian D. Gradientbased stochastic estimation of the density matrix. United States. doi:10.1063/1.5017741.
Wang, Zhentao, Cher, GiaWei, Barros, Kipton Marcos, and Batista, Cristian D. 2018.
"Gradientbased stochastic estimation of the density matrix". United States.
doi:10.1063/1.5017741.
@article{osti_1481135,
title = {Gradientbased stochastic estimation of the density matrix},
author = {Wang, Zhentao and Cher, GiaWei and Barros, Kipton Marcos and Batista, Cristian D.},
abstractNote = {Fast estimation of the singleparticle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. Here, we introduce a gradientbased probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zerotemperature metals, the stochastic error scales like S(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.},
doi = {10.1063/1.5017741},
journal = {Journal of Chemical Physics},
number = 9,
volume = 148,
place = {United States},
year = {2018},
month = {3}
}