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 Shull-Wollan Center
Fast estimation of the single-particle 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 gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature 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.
Wang, Zhentao, et al. "Gradient-based stochastic estimation of the density matrix." Journal of Chemical Physics, vol. 148, no. 9, Mar. 2018. https://doi.org/10.1063/1.5017741
Wang, Zhentao, Cher, Gia-Wei, Barros, Kipton Marcos, & Batista, Cristian D. (2018). Gradient-based stochastic estimation of the density matrix. Journal of Chemical Physics, 148(9). https://doi.org/10.1063/1.5017741
Wang, Zhentao, Cher, Gia-Wei, Barros, Kipton Marcos, et al., "Gradient-based stochastic estimation of the density matrix," Journal of Chemical Physics 148, no. 9 (2018), https://doi.org/10.1063/1.5017741
@article{osti_1481135,
author = {Wang, Zhentao and Cher, Gia-Wei and Barros, Kipton Marcos and Batista, Cristian D.},
title = {Gradient-based stochastic estimation of the density matrix},
annote = {Fast estimation of the single-particle 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 gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature 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},
url = {https://www.osti.gov/biblio/1481135},
journal = {Journal of Chemical Physics},
issn = {ISSN 0021-9606},
number = {9},
volume = {148},
place = {United States},
publisher = {American Institute of Physics (AIP)},
year = {2018},
month = {03}}
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2011https://doi.org/10.1098/rsta.2012.0483