Unwrapping Complex Phases to Address Sign Problems in Lattice Calculations

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.