171 research outputs found
Phase Unwrapping and One-Dimensional Sign Problems
Sign problems in path integrals arise when different field configurations
contribute with different signs or phases. Phase unwrapping describes a family
of signal processing techniques in which phase differences between elements of
a time series are integrated to construct non-compact unwrapped phase
differences. By combining phase unwrapping with a cumulant expansion, path
integrals with sign problems arising from phase fluctuations can be
systematically approximated as linear combinations of path integrals without
sign problems. This work explores phase unwrapping in zero-plus-one-dimensional
complex scalar field theory. Results with improved signal-to-noise ratios for
the spectrum of scalar field theory can be obtained from unwrapped phases, but
the size of cumulant expansion truncation errors is found to be undesirably
sensitive to the parameters of the phase unwrapping algorithm employed. It is
argued that this numerical sensitivity arises from discretization artifacts
that become large when phases fluctuate close to singularities of a complex
logarithm in the definition of the unwrapped phase.Comment: 42 pages, 16 figures. Journal versio
Unwrapping phase fluctuations in one dimension
Correlation functions in one-dimensional complex scalar field theory provide
a toy model for phase fluctuations, sign problems, and signal-to-noise problems
in lattice field theory. Phase unwrapping techniques from signal processing are
applied to lattice field theory in order to map compact random phases to
noncompact random variables that can be numerically sampled without sign or
signal-to-noise problems. A cumulant expansion can be used to reconstruct
average correlation functions from moments of unwrapped phases, but points
where the field magnitude fluctuates close to zero lead to ambiguities in the
definition of the unwrapped phase and significant noise at higher orders in the
cumulant expansion. Phase unwrapping algorithms that average fluctuations over
physical length scales improve, but do not completely resolve, these issues in
one dimension. Similar issues are seen in other applications of phase
unwrapping, where they are found to be more tractable in higher dimensions.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with
arXiv:1806.0183
Exponential reduction of finite volume effects with twisted boundary conditions
Flavor-twisted boundary conditions can be used for exponential reduction of
finite volume artifacts in flavor-averaged observables in lattice QCD
calculations with light quark flavor symmetry. Finite volume artifact
reduction arises from destructive interference effects in a manner closely
related to the phase averaging which leads to large volume independence.
With a particular choice of flavor-twisted boundary conditions, finite volume
artifacts for flavor-singlet observables in a hypercubic spacetime volume are
reduced to the size of finite volume artifacts in a spacetime volume with
periodic boundary conditions that is four times larger.Comment: 18 pages, no figure
Baryons, multi-hadron systems, and composite dark matter in non-relativistic QCD
We provide a formulation of potential non-relativistic quantum chromodynamics
(pNRQCD) suitable for calculating binding energies and matrix elements of
generic hadron and multi-hadron states made of heavy quarks in gauge
theory using quantum Monte Carlo techniques. We compute masses of quarkonium
and triply-heavy baryons in order to study the perturbative convergence of
pNRQCD and validate our numerical methods. Further, we study models
of composite dark matter and provide simple power series fits to our pNRQCD
results that can be used to relate dark meson and baryon masses to the
fundamental parameters of these models. For many systems comprised entirely of
heavy quarks, the quantum Monte Carlo methods employed here are less
computationally demanding than lattice field theory methods, although they
introduce additional perturbative approximations. The formalism presented here
may therefore be particularly useful for predicting composite dark matter
properties for a wide range of and heavy fermion masses.Comment: 39 pages, 24 figure
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