Semistochastic Projector Monte Carlo Method

Authors

F. R. Petruzielo
A. A. Holmes
Hitesh J. Changlani
M. P. Nightingale, University of Rhode IslandFollow
C. J. Umrigar

Document Type

Article

Date of Original Version

12-7-2012

Abstract

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochastic method, the semistochastic approach significantly reduces the computational time required to obtain the eigenvalue to a specified statistical uncertainty. This is demonstrated by the application of the semistochastic quantum Monte Carlo method to systems with a sign problem: the fermion Hubbard model and the carbon dimer.

Citation/Publisher Attribution

F. R. Petruzielo, A. A. Holmes, Hitesh J. Changlani, M. P. Nightingale, and C. J. Umrigar. (2012). "Semistochastic Projector Monte Carlo Method." Physical Review Letters, 109(23), 230201. doi: 10.1103/PhysRevLett.109.230201

Available at: http://dx.doi.org/10.1103/PhysRevLett.109.230201

Publisher Statement

© 2012 The American Physical Society