Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks

Abstract

The Banks--Casher relation links the spontaneous breaking of chiral symmetry in QCD to the presence of a non-zero density of quark modes at the low end of the spectrum of the Dirac operator. Spectral observables like the number of modes in a given energy interval are renormalizable and can therefore be computed using the Wilson formulation of lattice QCD even though the latter violates chiral symmetry at energies on the order of the inverse lattice spacing. Using numerical simulations, we find (in two-flavour QCD) that the low quark modes do condense in the expected way. In particular, the chiral condensate can be accurately calculated simply by counting the low modes on large lattices. Other spectral observables can be considered as well and have a potentially wide range of uses.

arXiv commentPlain TeX, 30 pages, 5 figures

References in corpus (23)

• Chiral symmetry and O(a) improvement in lattice QCD
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• O(a) improvement of the axial current in lattice QCD to one-loop order of perturbation theory
• O(a) improvement of lattice QCD with two flavors of Wilson quarks
• Further results on O(a) improved lattice QCD to one-loop order of perturbation theory
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Partially quenched chiral perturbation theory without ${\Phi }_0$
• Numerical techniques for lattice QCD in the $\epsilon$--regime
• Non-perturbative quark mass renormalization in two-flavor QCD
• Stability of lattice QCD simulations and the thermodynamic limit
• QCD with light Wilson quarks on fine lattices (I): first experiences and physics results
• Topological effects in QCD and the problem of short-distance singularities
• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Convergence of the chiral expansion in two-flavor lattice QCD
• Two-flavor lattice QCD in the epsilon-regime and chiral Random Matrix Theory
• Topological susceptibility in full QCD with Ginsparg-Wilson fermions
• Non-perturbative improvement of the axial current for dynamical Wilson fermions
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Further one-loop results in O(a) improved lattice QCD
• The condensate for two dynamical chirally improved quarks in QCD

Cited by in corpus (85)

• Properties and uses of the Wilson flow in lattice QCD
• FLAG Review 2019
• FLAG Review 2021
• Review of lattice results concerning low energy particle physics
• Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective
• Axion phenomenology and $\theta$-dependence from $N_f=2+1$ lattice QCD
• Hyperscaling relations in mass-deformed conformal gauge theories
• The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions
• The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions
• Lattice tests of beyond Standard Model dynamics
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Scale-dependent mass anomalous dimension from Dirac eigenmodes
• Microscopic Spectrum of the Wilson Dirac Operator
• Universality of the topological susceptibility in the SU(3) gauge theory
• Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD
• Non-Gaussianities in the topological charge distribution of the SU(3) Yang--Mills theory
• Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature
• Topology in full QCD at high temperature: a multicanonical approach
• A precise determination of the psibar-psi anomalous dimension in conformal gauge theories
• Symmetries of hadrons after unbreaking the chiral symmetry
• Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow
• Quark disconnected diagrams in chiral perturbation theory
• Unbreaking chiral symmetry
• Landau levels in QCD
• Non-perturbative volume-reduction of large-N QCD with adjoint fermions
• Determination of the chiral condensate from QCD Dirac spectrum on the lattice
• Determination of the chiral condensate from 2+1-flavor lattice QCD
• Chiral condensate from the twisted mass Dirac operator spectrum
• Poisson to Random Matrix Transition in the QCD Dirac Spectrum
• Topology and axions in QCD
• Eigenvalue spectra of QCD and the fate of $U_A(1)$ breaking towards the chiral limit
• Topological susceptibility of $N_f=2+1$ QCD from staggered fermions spectral projectors at high temperatures
• The nucleon electric dipole moment with the gradient flow: the $\theta$-term contribution
• Non-perturbative renormalization in coordinate space for $N_f=2$ maximally twisted mass fermions with tree-level Symanzik improved gauge action
• Non-perturbative Test of the Witten-Veneziano Formula from Lattice QCD
• Contribution of the QCD $\Theta$-term to nucleon electric dipole moment
• Neutron electric dipole moment using lattice QCD simulations at the physical point
• Spectral density of the Dirac operator in two-flavour QCD
• The chiral condensate from renormalization group optimized perturbation
• Large-N reduction in QCD with two adjoint Dirac fermions
• Topological susceptibility from twisted mass fermions using spectral projectors and the gradient flow
• Lattice study of large $N_c$ QCD
• Chiral Symmetry Breaking on the Lattice
• Frequency-splitting estimators of single-propagator traces
• Probing the chiral regime of Nf=2 QCD with mixed actions
• Chiral symmetry breaking in QCD Lite
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$ from lattice QCD with SU(3) flavor symmetry
• Global Structure of Conformal Theories in the SU(3) Gauge Theory
• Correlation and localization properties of topological charge density and the pseudoscalar glueball mass in SU(3) lattice Yang-Mills theory
• The Realization of the Sharpe-Singleton Scenario
• Topological susceptibility in lattice Yang-Mills theory with open boundary condition
• Lattice computation of the Dirac eigenvalue density in the perturbative regime of QCD
• Anomalous dimensions on the lattice
• GMOR-like relation in IR-conformal gauge theories
• Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory
• Topological susceptibility from the twisted mass Dirac operator spectrum
• Determining low-energy constants in partially quenched Wilson chiral perturbation theory
• Topology via Spectral Projectors with Staggered Fermions
• Infrared fixed point of SU(2) gauge theory with six flavors
• Anderson localization in QCD-like theories
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• Connected and Disconnected Contractions in Pion-Pion Scattering
• Banks-Casher-type relation for the BCS gap at high density
• Revisiting the pion's scalar form factor in chiral perturbation theory
• The gradient flow running coupling in SU(2) gauge theory with $N_f=8$ fundamental flavors
• Localization properties of Dirac modes at the Roberge-Weiss phase transition
• Low energy properties of SU(2) gauge theory with N_f = 3/2 flavours of adjoint fermions
• Quark mass anomalous dimension and ${\Lambda }_{\overline{\text{MS}}}$ from the twisted mass Dirac operator spectrum
• Chiral Condensate and Spectral Density at full five-loop and partial six-loop orders of Renormalization Group Optimized Perturbation
• Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition
• Localisation of Dirac modes in gauge theories and Goldstone's theorem at finite temperature
• New insight on the quark condensate beyond chiral limit
• Sign problem and the chiral spiral on the finite-density lattice
• Features of a 2d Gauge Theory with Vanishing Chiral Condensate
• Short distance singularities and automatic O($a$) improvement: the cases of the chiral condensate and the topological susceptibility
• Chiral symmetry breaking and quark confinement in the nilpotency expansion of QCD
• A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD
• Alternatives to the stochastic "noise vector" approach
• Dirac-mode analysis for quark number density and its application for deconfinement transition
• Status of a minimal composite Higgs theory
• Topology in the 2d Heisenberg Model under Gradient Flow
• Dirac spectral density and mass anomalous dimension in 2+1 flavor QCD
• Conformal window in SU(2) with fundamental fermions
• Microscopic Encoding of Macroscopic Universality in QCD Chiral Phase Transition
• Gluon Condensate via Dirac Spectral Density: IR Phase, Scale Anomaly and IR Decoupling