Gradient-based stochastic estimation of the density matrix

Abstract

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 $r_{ij}$ 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. 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.

References in corpus (6)

• The Kernel Polynomial Method
• Random phase vector for calculating the trace of a large matrix
• Novel magnetic orderings in the kagome Kondo-lattice model
• An efficient and accurate decomposition of the Fermi operator
• Semiclassical dynamics of spin density waves
• SIESTA-PEXSI: Massively parallel method for efficient and accurate \textit{ab initio} materials simulation without matrix diagonalization

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