Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors

Abstract

We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following spectral observables: the level density of the Hermitian Wilson Dirac operator, the distribution of chirality over the real eigenvalues, and the chiral condensate for the quenched as well as for the unquenched theory. We provide analytical expressions for all these quantities. Moreover we derive constraints for the level density of the real eigenvalues of the non-Hermitian Wilson Dirac operator and the number of additional real modes. The latter is a good measure for the strength of lattice artefacts. All computations are confirmed by Monte Carlo simulations of the corresponding random matrix theory which agrees with chiral perturbation theory of two color QCD with Wilson fermions.

42 pages, 34 figures, two references added

References in corpus (9)

• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Superbosonization of invariant random matrix ensembles
• Higher representations on the lattice: perturbative studies
• Random matrices beyond the Cartan classification
• The epsilon regime with Wilson fermions
• Integration of Grassmann variables over invariant functions on flat superspaces
• Comparison of the superbosonization formula and the generalized Hubbard-Stratonovich transformation
• QCD-like technicolor on the lattice

Cited by in corpus (13)

• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Complex Langevin Simulation of a Random Matrix Model at Nonzero Chemical Potential
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Complex Langevin simulations of a finite density matrix model for QCD
• Kondo effect with Wilson fermions
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Universal Distribution of Would-be Topological Zero Modes in Coupled Chiral Systems
• Universal distributions from non-Hermitian Perturbation of Zero-Modes
• Discretization effects in $N_c=2$ QCD and Random Matrix Theory
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Universal Broadening of Zero Modes: A General Framework and Identification