Phase Unwrapping and One-Dimensional Sign Problems

Abstract

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.

42 pages, 16 figures. Journal version

References in corpus (21)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Nuclear Physics from Lattice QCD
• Most Strange Dibaryon from Lattice QCD
• Baryon-Baryon Interactions and Spin-Flavor Symmetry from Lattice Quantum Chromodynamics
• Phase of the Fermion Determinant at Nonzero Chemical Potential
• High Statistics Analysis using Anisotropic Clover Lattices: (II) Three-Baryon Systems
• On the existence of the critical point in finite density lattice QCD
• The QCD Sign Problem for Small Chemical Potential
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Method for simulating O(N) lattice models at finite density
• Nuclear modification of scalar, axial and tensor charges from lattice QCD
• A local factorization of the fermion determinant in lattice QCD
• Lefschetz-thimble techniques for path integral of zero-dimensional $O(n)$ sigma models
• First lattice QCD study of the gluonic structure of light nuclei
• Symmetries and exponential error reduction in Yang-Mills theories on the lattice
• Signal/noise enhancement strategies for stochastically estimated correlation functions
• Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
• Baryon interactions from lattice QCD with physical quark masses -- Nuclear forces and $\Xi \Xi$ forces --
• Uncertainty Quantification in Lattice QCD Calculations for Nuclear Physics
• Distribution of Canonical Determinants in QCD
• New techniques and results for worldline simulations of lattice field theories

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