Year: 2026
Type: article
Abstract: High Resolution Image Download MS PowerPoint Slide Stochastic formulations of electronic-structure theory often reduce computational cost by replacing exact contractions with statistical estimates obtained from random samples, a procedure that inherently introduces random fluctuations and systematic bias. The fluctuations decay as M –1/2 with the number of samples M, whereas the bias generated in nonlinear or self-consistent settings decays as M –1 and can remain significant for moderate M . To control this bias we employ the jackknife-2 estimator, which reduces its leading term to O ( M − 2 ) with only modest extra cost. We examine bias formation and removal in three settings: (i) stochastic treatments of the Markovian master equation using bundled dissipators, (ii) stochastic Kohn–Sham density functional theory for warm dense hydrogen, and (iii) stochastic evaluation of the Hubbard-model partition function. The first two settings have been presented in earlier works; accordingly, we review them only briefly and focus primarily on the issue of bias control. The Hubbard-model application is entirely new. For this case, we present two approaches: a direct estimator, which has large variance but no bias, and a “midway transition probability” (ΣMTP) estimator, which has smaller variance but introduces bias. Applying the jackknife-2 procedure to the ΣMTP estimator controls this bias and yields a substantially lower total error than the direct estimator. Across all cases, jackknife bias removal markedly improves the accuracy and reliability of stochastic electronic-structure calculations without increasing the computational cost.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,500
Funder: Israel Science Foundation
Awards: G1032849733, G1295360210, G3883245813
OpenAlex ID: W7138244713