Gradient-based stochastic estimation of the density matrix

Wang, Zhentao; Cher, Gia-Wei; Barros, Kipton Marcos; Batista, Cristian D.

doi:10.1063/1.5017741

Title: Gradient-based stochastic estimation of the density matrix

Journal Article · Mon Mar 05 00:00:00 EST 2018 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.5017741· OSTI ID:1481135

Wang, Zhentao ^[1]; Cher, Gia-Wei ^[2];

^[3]; Batista, Cristian D. ^[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 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1481135

Alternate ID(s):: OSTI ID: 1423724

Report Number(s):: LA-UR-17-30801

Journal Information:: Journal of Chemical Physics, Vol. 148, Issue 9; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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