Bulletin of the American Physical Society
APS April Meeting 2019
Volume 64, Number 3
Saturday–Tuesday, April 13–16, 2019; Denver, Colorado
Session Q14: Nuclear Theory
10:45 AM–12:09 PM,
Monday, April 15, 2019
Sheraton
Room: Plaza Court 3
Sponsoring
Unit:
DNP
Chair: Gerald A. Miller, University of Washington
Abstract: Q14.00001 : Unwrapping Complex Phases to Address Sign Problems in Lattice Calculations*
10:45 AM–10:57 AM
View Presentation Abstract
Presenter:
Gurtej Kanwar
(Massachusetts Institute of Technology)
Authors:
William Detmold
(Massachusetts Institute of Technology)
Gurtej Kanwar
(Massachusetts Institute of Technology)
Michael L Wagman
(Massachusetts Institute of Technology)
Lattice QCD (LQCD) allows non-perturbative theoretical predictions of properties of nuclear states directly from QCD. LQCD estimates of correlators with non-zero baryon number suffer from a signal-to-noise problem at large time separations, limiting the precision of many calculations. Previous work has shown that this is due to a widening distribution of complex phases. Standard estimators suffer from a sign problem and perform exponentially poorly as the distribution approaches uniform. We apply a technique known as "phase unwrapping" to LQCD correlators, to produce an unwrapped phase distribution over the reals. A cumulant expansion provides convergent positive estimates of correlators.
Applied to the simple harmonic oscillator as a toy model, we demonstrate an exponential improvement in signal-to-noise at leading order in the cumulant expansion and describe a good unwrapping scheme choice that precisely estimates ground state energies. We discuss incorporating the positive-definite estimate of the correlation function into the Monte Carlo sampling to provide an improvement free of systematic bias from truncation error.
*Supported by DoE (No. de-sc0010495 and No. de-sc0011090), SciDAC4 (No. de-sc0018121), and the MIT Pappalardo Fellowship (MLW).
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