Uncertainty quantification in lattice QCD calculations for nuclear physics

Beane, Silas R.; Detmold, Will; Orginos, Kostas; Savage, Martin J.

doi:10.1088/0954-3899/42/3/034022

Cited by 64 publications

(110 citation statements)

References 147 publications

(219 reference statements)

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“…This is well-known technology and is a "workhorse" in the analysis of LQCD calculations. Typically, t J corresponds to one temporal lattice spacing, and the jackknife and bootstrap resampling techniques are used to generate covariance matrices in the plateau interval used to extract the ground-state energy from a correlated χ 2 -minimization [8,9,31]. 4 The energy can be extracted from an exponential fit to the correlation function or by a direct fit to the effective mass itself.…”

Section: Relevant Aspects Of Standard Analysis Methods Of Correlamentioning

confidence: 99%

“…This suggests that δE should be set by the gap between the ground state and first excited state with appropriate quantum numbers. 8 e Ri(t+1) can similarly be split into an approximately decorrelated product. Performing this split with regions [0, t − ∆t] and [t − ∆t, t + 1] gives e Ri(t+1) = e Ri(0)+∆Ri(t−∆t,t−∆t) e ∆Ri(t+1,∆t+1) 1 + O e −δE∆t .…”

Section: An Improved Estimatormentioning

confidence: 99%

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Statistics of baryon correlation functions in lattice QCD

Wagman

Savage²

2017

Phys. Rev. D

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A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and "Lévy flights", are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem re-emerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

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Section: Relevant Aspects Of Standard Analysis Methods Of Correlamentioning

confidence: 99%

Section: An Improved Estimatormentioning

confidence: 99%

Statistics of baryon correlation functions in lattice QCD

Wagman

Savage²

2017

Phys. Rev. D

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“…In π /EFT these correlations are understood [21,22] by the fact that, if the two-body input is fixed, three-body predictions in the doublet channel still depend on one parameter in LO, which determines the three-body force in Eq. (1). As this parameter is varied, three-body observables sensitive to the LO threebody force all change in a correlated way.…”

Section: A the Three-body Sectormentioning

confidence: 99%

“…Although there seem to be ways around this problem [1], large A also requires that longer distances be covered by the lattice, since the nuclear volume increases with A. As in other areas of physics, it is profitable to change to a more effective description, in this case to an effective field theory (EFT) involving nucleons as degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Spectra and scattering of light lattice nuclei from effective field theory

et al. 2015

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An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two-and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the alpha-particle binding energy. For mπ=510 MeV we obtain, respectively, 4 anD = 2.3 ± 1.3 fm, 2 anD = 2.2 ± 2.1 fm, and B α = 35 ± 22 MeV, while for mπ=805 MeV 4 anD = 1.6 ± 1.3 fm, 2 anD = 0.62 ± 1.0 fm, and B α = 94 ± 45 MeV are found. Phillips-and Tjon-like correlations to the triton binding energy are established. We find the theoretical uncertainty in the respective correlation bands to be independent of the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and alpha particle are discussed.

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“…Solving QCD on a lattice of discretized space-time in Euclidean space represents the only method to calculate nuclear observables from the QCD Lagrangian [1]. Numerical calculations are only feasible in a finite box where the energy spectrum is discrete.…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo calculations of two neutrons in finite volume

Klos¹,

Lynn²,

Tews³

et al. 2016

Phys. Rev. C

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Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground-and excited-state energies for different box sizes.

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Uncertainty quantification in lattice QCD calculations for nuclear physics

Cited by 64 publications

References 147 publications

Statistics of baryon correlation functions in lattice QCD

Statistics of baryon correlation functions in lattice QCD

Spectra and scattering of light lattice nuclei from effective field theory

Quantum Monte Carlo calculations of two neutrons in finite volume

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