Signal/noise enhancement strategies for stochastically estimated correlation functions

We develop strategies for enhancing the signal/noise ratio for stochastically sampled correlation functions. The techniques are general and offer a wide range of applicability. We demonstrate the potential of the approach with a generic two-state system, and then explore the practical applicability of the method for single hadron correlators in lattice quantum chromodynamics. In the latter case, we determine the ground state energies of the pion, proton, and delta baryon, as well as the ground and first excited state energy of the rho meson using matrices of correlators computed on an exemplary ensemble of anisotropic gauge configurations. In the majority of cases, we find a modest reduction in the statistical uncertainties on extracted energies compared to conventional variational techniques. However, in the case of the delta baryon, we achieve a factor of three reduction in statistical uncertainties. The variety of outcomes achieved for single hadron correlators illustrates an inherent dependence of the method on the properties of the system under consideration and the operator basis from which the correlators are constructed.Comment: 40 pages, 21 figures; revisions made to the abstract and Section VI C, one additional figure and five tables added; published versio

Lattice theory for nonrelativistic fermions in one spatial dimension

I derive a loop representation for the canonical and grand-canonical partition functions for an interacting four-component Fermi gas in one spatial dimension and an arbitrary external potential. The representation is free of the "sign problem" irrespective of population imbalance, mass imbalance, and to a degree, sign of the interaction strength. This property is in sharp contrast with the analogous three-dimensional two-component interacting Fermi gas, which exhibits a sign problem in the case of unequal masses, chemical potentials, and repulsive interactions. The one-dimensional system is believed to exhibit many phenomena in common with its three-dimensional counterpart, including an analog of the BCS-BEC crossover, and nonperturbative universal few- and many-body physics at scattering lengths much larger than the range of interaction, making the theory an interesting candidate for numerical study. Positivity of the probability measure for the partition function allows for a mean-field treatment of the model; here, I present such an analysis for the interacting Fermi gas in the SU(4) (unpolarized, mass-symmetric) limit, and demonstrate that there exists a phase in which a continuum limit may be defined.Comment: 12 pages, 6 figures, references adde