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Microscopic spectrum of the Wilson Dirac operator.
P H Damgaard1, K Splittorff, J J M Verbaarschot
1Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark.
Physical Review Letters
|January 15, 2011
Summary
We calculated spectral density for the Wilson Dirac operator using chiral perturbation theory. This provides a new method for lattice gauge theory analysis at finite lattice spacing.
Area of Science:
- * Quantum Chromodynamics (QCD)
- * Lattice Gauge Theory
- * Chiral Symmetry
Background:
- * The Wilson Dirac operator is crucial for lattice QCD simulations.
- * Understanding its spectral density is key to analyzing chiral symmetry breaking.
- * Previous methods faced challenges with finite lattice spacing and volume effects.
Purpose of the Study:
- * To calculate the leading contribution to the spectral density of the Wilson Dirac operator.
- * To develop analytical expressions for spectral density incorporating volume and lattice spacing corrections.
- * To introduce a chiral random matrix theory model that matches these analytical results.
Main Methods:
- * Application of chiral perturbation theory.
- * Derivation of universal scaling functions for corrections.
- * Development of a chiral random matrix theory framework.
Main Results:
- * Analytical expressions for spectral density at the scale of average level spacing.
- * A novel chiral random matrix theory that reproduces the calculated spectral density.
- * Identification of volume and lattice spacing corrections via scaling functions.
Conclusions:
- * The study presents a novel approach to the infinite-volume limit in lattice gauge theory at finite lattice spacing.
- * The developed chiral random matrix theory offers a new tool for analyzing lattice QCD data.
- * New methods are established for extracting coefficients of Wilson chiral perturbation theory.
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