721 research outputs found
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
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