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Related Experiment Videos

Overlap Dirac operator at nonzero chemical potential and random matrix theory.

Jacques Bloch1, Tilo Wettig

  • 1Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany.

Physical Review Letters
|August 16, 2006
PubMed
Summary

We introduce quark chemical potential into the overlap Dirac operator, finding it maintains exact zero modes and paired eigenvalues. Lattice data align with non-Hermitian chiral random matrix theory predictions.

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Area of Science:

  • Quantum Chromodynamics (QCD)
  • Lattice Field Theory
  • Chiral Symmetry

Background:

  • The overlap Dirac operator is crucial for lattice QCD simulations, preserving chiral symmetry.
  • Introducing a quark chemical potential is essential for studying dense nuclear matter but poses theoretical challenges.
  • Understanding the spectral properties of Dirac operators in the presence of chemical potential is key.

Purpose of the Study:

  • To develop a method for incorporating quark chemical potential into the overlap Dirac operator.
  • To investigate the spectral properties and zero modes of this modified operator.
  • To compare lattice results with theoretical predictions from non-Hermitian chiral random matrix theory.

Main Methods:

  • Modification of the overlap Dirac operator to include a quark chemical potential.

Related Experiment Videos

  • Analysis of the operator's symmetry properties, including the Ginsparg-Wilson relation and Hermiticity.
  • Lattice QCD simulations to compute the spectral density of the modified operator.
  • Comparison of spectral data with analytical predictions from non-Hermitian chiral random matrix theory.

    • Main Results:

    • The modified overlap Dirac operator satisfies a Ginsparg-Wilson relation and possesses exact zero modes.
    • The operator is no longer gamma5 Hermitian, but its nonreal eigenvalues appear in pairs.
    • Lattice data for the spectral density at small eigenvalues show agreement with non-Hermitian chiral random matrix theory for both trivial and nontrivial topology.
    • An explanation is provided for the observed change in the number of zero modes as a function of chemical potential.

    Conclusions:

    • A consistent method for introducing quark chemical potential in the overlap Dirac operator has been established.
    • The study validates the applicability of non-Hermitian chiral random matrix theory to lattice QCD spectral properties.
    • The findings offer insights into the behavior of Dirac operator zero modes under varying chemical potentials.