Spontaneous Flavor and Parity Breaking with Wilson Fermions

Abstract

We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for two-flavor QCD. We argue that, as originally suggested by Aoki, there is a phase in which flavor and parity are spontaneously broken. Recent numerical results on the spectrum of the overlap Hamiltonian have been interpreted as evidence against Aoki's conjecture. We show that they are in fact consistent with the presence of a flavor-parity broken ``Aoki phase''. We also show how, as the continuum limit is approached, one can study the lattice theory using the continuum chiral Lagrangian supplemented by additional terms proportional to powers of the lattice spacing. We find that there are two possible phase structures at non-zero lattice spacing: (1) there is an Aoki phase of width $\Delta m_0\sim a^3$ with two massless Goldstone pions; (2) there is no symmetry breaking, and all three pions have an equal non-vanishing mass of order $a$. Present numerical evidence suggests that the former option is realized for Wilson fermions. Our analysis then predicts the form of the pion masses and the flavor-parity breaking condensate within the Aoki phase. Our analysis also applies for non-perturbatively improved Wilson fermions.

22 pages, LaTeX, 5 figures (added several references and a comment)

References in corpus (5)

• Probing the Region of Massless Quarks in Quenched Lattice QCD using Wilson Fermions
• A new method to measure the chiral condensate in lattice QCD using Wilson fermions
• Phase Structure of Lattice QCD with Wilson fermion at Finite Temperature
• On the Parity-Flavor-Breaking Phase in QCD With Two Flavors of Wilson Fermions
• Non-perturbative improvement of operators with Wilson fermions

Cited by in corpus (226)

• FLAG Review 2019
• Chirally improving Wilson fermions - I. O(a) improvement
• Review of lattice results concerning low energy particle physics
• Chiral Perturbation Theory and Baryon Properties
• Chirally improving Wilson fermions II. Four-quark operators
• Dynamical Twisted Mass Fermions with Light Quarks: Simulation and Analysis Details
• Partial Flavor Symmetry Restoration for Chiral Staggered Fermions
• Physical Results from Unphysical Simulations
• Dynamical Twisted Mass Fermions with Light Quarks
• Light Hadron Masses from Lattice QCD
• Chiral perturbation theory for the Wilson lattice action
• Chiral perturbation theory at O(a^2) for lattice QCD
• Anomalous chirality fluctuations in the initial stage of heavy ion collisions and parity odd bubbles
• I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD
• Nucleon axial form factors using lattice QCD simulations with a physical value of the pion mass
• Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
• On the order of the QCD chiral phase transition for different numbers of quark flavours
• Simulating twisted mass fermions at physical light, strange and charm quark masses
• Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson Valence Quarks
• Aspects of Chiral Symmetry and the Lattice
• Twisted mass chiral perturbation theory at next-to-leading order
• QCD with light Wilson quarks on fine lattices (I): first experiences and physics results
• Simulations with different lattice Dirac operators for valence and sea quarks
• Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations
• Microscopic Spectrum of the Wilson Dirac Operator
• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• Low-lying baryon masses using $N_f=2$ twisted mass clover-improved fermions directly at the physical point
• Localization in Lattice QCD
• The phase diagram of twisted mass lattice QCD
• Reducing cutoff effects in maximally twisted lattice QCD close to the chiral limit
• Lattice Quantum Gravity and Asymptotic Safety
• Pion mass splitting and phase structure in Twisted Mass QCD
• Heavy physics contributions to neutrinoless double beta decay from QCD
• Sp(4) gauge theories on the lattice: $N_f=2$ dynamical fundamental fermions
• Two-flavor QCD simulation with exact chiral symmetry
• Electromagnetic and spin polarisabilities in lattice QCD
• Light quark masses from unquenched lattice QCD
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• On the phase structure of twisted mass lattice QCD
• Chiral perturbation theory with Wilson-type fermions including $a^2$ effects: $N_f=2$ degenerate case
• Twisted-mass QCD, O(a) improvement and Wilson chiral perturbation theory
• The phase structure of lattice QCD with two flavours of Wilson quarks and renormalization group improved gluons
• Singular values of the Dirac operator in dense QCD-like theories
• Twisted mass quarks and the phase structure of lattice QCD
• Two Meson Systems with Ginsparg-Wilson Valence Quarks
• Sp(4) gauge theories on the lattice: Quenched fundamental and antisymmetric fermions
• Lattice QCD with Ginsparg-Wilson fermions
• Higher representations on the lattice: perturbative studies
• Staggered Chiral Perturbation Theory at Next-to-Leading Order
• Scattering lengths for two pseudoscalar meson systems
• Localization and chiral symmetry in 2+1 flavor domain wall QCD
• Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program
• Chiral properties of domain-wall quarks in quenched QCD
• Baryons with Ginsparg-Wilson quarks in a staggered sea
• Effective field theories for QCD with rooted staggered fermions
• Non-perturbative volume-reduction of large-N QCD with adjoint fermions
• Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks
• Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks
• Numerical simulation of QCD with u, d, s and c quarks in the twisted-mass Wilson formulation
• Approach to the Continuum Limit of the Quenched Hermitian Wilson-Dirac Operator
• Localization properties of lattice fermions with plaquette and improved gauge actions
• Universality of Mixed Action Extrapolation Formulae
• Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory
• $F_K/F_{\pi }$ from Möbius domain-wall fermions solved on gradient-flowed HISQ ensembles
• Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions
• A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Aoki Phases in the Lattice Gross-Neveu Model with Flavored Mass terms
• Strange quarks in quenched twisted mass lattice QCD
• Lattice Spacing Dependence of the First Order Phase Transition for Dynamical Twisted Mass Fermions
• Light quarks with twisted mass fermions
• Observations on discretization errors in twisted-mass lattice QCD
• Mobility edge in lattice QCD
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• Filtered overlap: speedup, locality, kernel non-normality and Z_A~1
• An accurate calculation of the nucleon axial charge with lattice QCD
• Exploring the phase structure of lattice QCD with twisted mass quarks
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Spontaneous Parity Violation in QCD At Finite Temperature: On the Inapplicability of the Vafa-Witten Theorem
• On the consistency of the Aoki-phase
• Light hadron spectroscopy in two-flavor QCD with small sea quark masses
• Large-N reduction in QCD with two adjoint Dirac fermions
• Vafa-Witten theorem, vector meson condensates and magnetic-field-induced electromagnetic superconductivity of vacuum
• SU(2) Low-Energy Constants from Mixed-Action Lattice QCD
• Calculation of the strange quark mass using domain wall fermions
• The epsilon regime with Wilson fermions
• Light meson electromagnetic form factors from three-flavor lattice QCD with exact chiral symmetry
• Effective theory for quenched lattice QCD and the Aoki phase
• Interactions of $\pi K$, $\pi \pi K$ and $KK\pi$ systems at maximal isospin from lattice QCD
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Observations on the Wilson fermions in the epsilon regime
• Hadron masses in QCD with one quark flavour
• Going chiral: overlap versus twisted mass fermions
• Chiral perturbation theory at non-zero lattice spacing
• Rooted staggered fermions: good, bad or ugly?
• Probing the chiral regime of Nf=2 QCD with mixed actions
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Numerical simulations with two flavours of twisted-mass Wilson quarks and DBW2 gauge action
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Reducing Chiral Symmetry Violations in Lattice QCD with Domain-Wall Fermions
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• Parton Distribution Functions with Twisted Mass Fermions
• Confinement, chiral symmetry, and the lattice
• Orbifold equivalence for finite density QCD and effective field theory
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
• Chiral logs in twisted mass lattice QCD with large isospin breaking
• Phase structure for lattice fermions with flavored chemical potential terms
• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Nucleon and Delta masses in twisted mass chiral perturbation theory
• Bulk first-order phase transition in three-flavor lattice QCD with $O(a)$-improved Wilson fermion action at zero temperature
• Validity Of The Vafa-Witten Proof On Absence Of Spontaneous Parity Breaking In QCD
• The renormalization group step scaling function of the 2-flavor SU(3) sextet model
• Twisted Mass Finite Volume Effects
• Wilson fermions with chirally twisted mass
• Axionic Antiferromagnetic Insulator Phase in a Correlated and Spin-Orbit Coupled System
• Lattice QCD Inputs for Nuclear Double Beta Decay
• Baryon masses at O(a^2) in chiral perturbation theory
• Electron Correlation Induced Spontaneous Symmetry Breaking and Weyl Semimetal Phase in a Strongly Spin-Orbit Coupled System
• Phase structure of thermal lattice QCD with N_f=2 twisted mass Wilson fermions
• The Realization of the Sharpe-Singleton Scenario
• Pion scattering in Wilson ChPT
• Pion Scattering in Wilson Chiral Perturbation Theory
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• The Microscopic Twisted Mass Dirac Spectrum
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Automatic O(a) improvement for twisted-mass QCD in the presence of spontaneous symmetry breaking
• Applications of Chiral Perturbation theory to lattice QCD
• QCD phase diagram with 2-flavor lattice fermion formulations
• Determining low-energy constants in partially quenched Wilson chiral perturbation theory
• Volume dependences from lattice chiral perturbation theory
• Analysis of Ward identities in supersymmetric Yang-Mills theory
• On the Vafa-Witten Theorem on Spontaneous Breaking of Parity
• Chiral Corrections to Hyperon Axial Form Factors
• Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at Finite Temperature and Chemical Potential
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• Phase structure of 2-dimensional topological insulators by lattice strong coupling expansion
• M_pi^2 versus m_q: comparing CP-PACS and UKQCD data to Chiral Perturbation Theory
• Chiral symmetry breaking with no bilinear condensate revisited
• The $\epsilon$-regime of dilaton chiral perturbation theory
• Pseudo scalar meson masses in Wilson Chiral Perturbation Theory for 2+1 flavors
• A Possible Aoki Phase for Staggered Fermions
• Vacuum alignment and lattice artifacts: Wilson fermions
• pi-pi Scattering in Twisted Mass Chiral Perturbation Theory
• Effective potentials, thermodynamics, and twisted mass quarks
• QCD with two flavors of Wilson fermions: The QCD vacuum, the Aoki vacuum and other vacua
• Strong Coupling Expansion in a Correlated Three-Dimensional Topological Insulator
• Twisted mass Lattice QCD
• Baryon chiral perturbation theory with Wilson fermions up to $\mathcal{O}(a^2)$ and discretization effects of latest $n_f=2+1$ LQCD octet baryon masses
• Before sailing on a domain-wall sea
• Varieties and properties of central-branch Wilson fermions
• Flavor symmetry breaking in lattice QCD with a mixed action
• Chiral Effective Theory Methods and their Application to the Structure of Hadrons from Lattice QCD
• Hadronic Electromagnetic Properties at Finite Lattice Spacing
• Fermion-scalar interactions with domain wall fermions
• Chiral perturbation theory for twisted mass QCD
• Baryon Number Dirac Spectrum in QCD
• Applying chiral perturbation to twisted mass Lattice QCD
• Chiral perturbation theory for partially quenched twisted mass lattice QCD
• A non-perturbative mechanism for elementary particle mass generation
• Topological chiral currents in the Gross-Neveu model extension
• Two dimensional lattice Gross--Neveu model with domain-wall fermions
• Vector and Axial Currents in Wilson Chiral Perturbation Theory
• Phase Structure of lattice SU(2)xU_S(1) three-dimensional Gauge Theory
• Spontaneous Parity Violation
• Predicting the Aoki Phase using the Chiral Lagrangian
• Strong-coupling Analysis of Parity Phase Structure in Staggered-Wilson Fermions
• Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory
• Kondo effect with Wilson fermions
• Isotropic and Anisotropic Lattice Spacing Corrections for I=2 pi-pi Scattering from Effective Field Theory
• Dynamical twisted mass fermions
• The Weakly Coupled Gross-Neveu Model with Wilson Fermions
• Low-energy constants in the chiral Lagrangian with baryon octet and decuplet fields from Lattice QCD data on CLS ensembles
• The Structure of the Aoki Phase at Weak Coupling
• Charmless chiral perturbation theory for N_f=2+1+1 twisted mass lattice QCD
• Parity realization in Vector-like theories from Fermion Bilinears
• Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor
• Effective Field Theory for the Anisotropic Wilson Lattice Action
• Partial Restoration of Flavor Symmetry for Chiral Staggered Fermions
• Phase diagram of non-degenerate twisted mass fermions
• Twisted mass lattice QCD with non-degenerate quark masses
• Low-energy constant $L_{10}$ in a two-representation lattice theory
• Scaling test of two-flavor O(a)-improved lattice QCD
• Is there an Aoki phase in quenched QCD?
• Vector meson masses in 2+1 flavor Wilson Chiral Perturbation Theory
• Unphysical phases in staggered chiral perturbation theory
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Vacuum alignment and lattice artifacts: staggered fermions
• The epsilon regime of chiral perturbation theory with Wilson-type fermions
• Elucidating the Vacuum Structure of the Aoki Phase
• First results with two light flavours of quarks with maximally twisted mass
• Twisted mass QCD at finite temperature
• Hadron Spectrum from Dynamical Lattice QCD Simulations
• Topics in Effective Field Theory for Lattice QCD
• Nf=2 Lattice QCD and Chiral Perturbation Theory
• QCD spectroscopy with three light quarks
• Hadron spectroscopy of twisted mass lattice QCD at beta = 6.0
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Two--dimensional lattice Gross--Neveu model with Wilson twisted mass fermions
• Finite isospin density probe for conformality
• Impossibility of spontaneous vector flavor symmetry breaking on the lattice
• An upper limit to the electric dipole moment of the neutron from lattice QCD
• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion
• Impact of electromagnetism on phase structure for Wilson and twisted-mass fermions including isospin breaking
• Symanzik effective action for Karsten-Wilczek minimally doubled fermions
• Chiral Perturbation Theory on the Lattice and its Applications
• Topics in Lattice QCD and Effective Field Theory
• Phase structure with nonzero ${\Theta }_{\mathrm{QCD}}$ and twisted mass fermions
• Chiral perturbation theory for twisted mass QCD at small quark mass
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• Lattice QCD at maximal twist
• Phase diagram of non-degenerate Wilson and twisted mass fermions
• The Leutwyler-Smilga relation on the lattice
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• Analyticity in theta and infinite volume limit of the topological susceptibility in SU(3) gauge theory
• Phase diagram of the single-flavor Gross--Neveu--Wilson model from the Grassmann corner transfer matrix renormalization group
• Flavor symmetry breaking in mixed-action QCD
• On the phase diagram of quenched QCD with Wilson fermions
• Isospin breaking and the chiral condensate
• New term in effective field theory at fixed topology
• The Effect of the Low Energy Constants on the Spectral Properties of the Wilson Dirac Operator