Effective noise reduction techniques for disconnected loops in Lattice QCD (0910.3970v2)

Abstract: Many Lattice QCD observables of phenomenological interest include so-called all-to-all propagators. The computation of these requires prohibitively large computational resources, unless they are estimated stochastically. This is usually done. However, the computational demand can often be further reduced by one order of magnitude by implementing sophisticated unbiased noise reduction techniques. We combine both well known and novel methods that can be applied to a wide range of problems. We concentrate on calculating disconnected contributions to nucleon structure functions, as one realistic benchmark example. In particular we determine the strangeness contributions to the nucleon, <N|ss|N>, and to the spin of the nucleon, Delta s.

Effective Noise Reduction Techniques for Disconnected Loops in Lattice QCD

The paper "Effective Noise Reduction Techniques for Disconnected Loops in Lattice QCD" explores advanced methods for reducing computational noise in Lattice Quantum Chromodynamics (QCD), particularly focusing on disconnected loop calculations. Disconnected loops are crucial for accurate nucleon structure function evaluations, including strangeness contributions, but their computation typically requires significant computational resources due to the necessity of evaluating all-to-all propagators.

Summary of Methods

The authors combine traditional and novel methods to improve the efficiency of stochastic estimations in Lattice QCD. The focus is on unbiased noise reduction techniques that aim to decrease the computational demand by an order of magnitude without affecting the accuracy of the results. The key methods discussed include:

• Stochastic Estimation: Employed to handle large computational demands, allowing the estimation of propagators across the lattice without direct inversion, which demands excessive memory.
• Partitioning: Decomposing the computation into subspaces to reduce variance, which can be beneficial when combined with additional methods like preconditioning.
• Truncated Solver Method (TSM): A novel technique allowing for large numbers of inexpensive estimates at reduced precision, which are later corrected by a smaller number of precise calculations, thus minimizing computational effort.
• Hopping Parameter Expansion (HPE): A method to remove noisy short-range contributions by exploiting the ultra-locality of the Wilson quark action.
• Truncated Eigenmode Acceleration (TEA): Reduces variance by focusing on low eigenmode contributions, which also leads to solver acceleration through deflation.

Numerical Results and Implications

The paper presents strong numerical results indicating substantial reductions in computational noise through combined techniques. The reduction in variance ranges widely but can reach factors as high as 30 times the baseline for complex nucleon structure calculations. Specifically, it focuses on the strangeness contributions to the nucleon, represented by key observables such as the axial charge $\Delta s$ and the scalar density $\langle N|\bar{s}s|N\rangle$.

The authors provide calculations showing that $\Delta s$ is negligibly small, suggesting minimal strangeness contributions to nucleon spin, which aligns with recent findings in deep inelastic scattering but contradicts earlier lattice results suggesting a larger negative value.

Future Developments

The techniques established in this paper for noise reduction in disconnected loop calculations could be crucial for future Lattice QCD studies, particularly for understanding nucleon structure and flavor singlet contributions. These methods can be extended to analyze larger lattices or configurations with smaller quark masses, guiding future developments in computational efficiency for similar quantum field theory applications.

Additionally, the scalability of these techniques for high-precision QCD simulations could facilitate further exploration into exotic hadron structures, meson spectra, and potentially improve the calculation accuracy for scattering states and multiquark systems.

Conclusion

The approach of combining noise reduction techniques, including TSM, partitioning, HPE, and TEA, offers significant gains in computational efficiency for disconnected loops in Lattice QCD. The paper's methods promise notable improvements in the precision of nucleon structure function calculations, and the results align well with recent experimental observations, offering a practical pathway for future theoretical and computational explorations in QCD and beyond.