Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0709.4416

The eigenvalue spectrum for dynamical Chirally Improved fermions

Martina Joergler·C. B. Lang
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for the overlap Dirac operator on these configurations with those for the Chirally Improved (CI) operator (studied earlier). Results of Random Matrix Theory allow us to determine the chiral condensate.

Explore related subjects

hep-lat

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Martina Joergler, C. B. Lang. 2007-09-27. The eigenvalue spectrum for dynamical Chirally Improved fermions. https://arxiv.org/abs/0709.4416

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

RG-Invariant Symmetry Ratio for QCD: A Study of $U(1)_A$ and Chiral Symmetry Restoration

We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio $κ_{AB}$, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ $κ_{AB}$ to investigate the relative strength of $SU(2)_L \times SU(2)_R$ chiral symmetry and $U(1)_A$ axial symmetry breaking in $N_f=2+1+1$ lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164--385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the $U(1)_A$-sensitive scalar--pseudoscalar channel ($κ_{PS}$), probing the $π$--$δ$ system; the $SU(2)_L \times SU(2)_R$-sensitive vector--axial-vector channel ($κ_{VA}$), probing the $ρ$--$a_1$ system; and an additional $U(1)_A$-sensitive tensor vector--axial-tensor vector channel ($κ_{TX}$), probing the $ρ_T$--$b_1$ system. At each lattice spacing we observe a clear hierarchy $κ_{PS} > κ_{VA} > κ_{TX}$. Since temperature and lattice spacing are not varied independently in the present ensembles, the lattice-spacing dependence of the hierarchy cannot be isolated, and a controlled continuum extrapolation is deferred to future work.

hep-lat↗
arXiv2026

Spontaneous chiral-symmetry breaking in four-dimensional QCD with $A_x=A_y=0$ projection in dimensional reduction gauge

We investigate spontaneous chiral-symmetry breaking in four-dimensional (4D) QCD in the dimensional reduction (DR) gauge, defined so as to minimize $R_{\mathrm{DR}}\equiv~\int d^{4}s ~ \mathrm{Tr} \left[ A_{x}^{2}(s) + A_{y}^{2}(s) \right]$. We consider ``$tz$-projection" of $A_{x,y}(s) \to 0$ and ``$xy$-projection" of $A_{t,z}(s) \to 0$, respectively, for the gauge configuration generated in the DR gauge, in a similar sense to Abelian, monopole and photon projections in the maximally Abelian gauge. The chiral condensate is estimated from the low-lying Dirac-eigenvalue density $ρ(λ)$ using the Banks-Casher relation. By the $tz$-projection in the DR gauge, the chiral condensate is largely reserved. In contrast, the chiral condensate becomes zero by the $xy$-projection in the DR gauge. This indicates that $A_{t}(s)$ and $A_{z}(s)$ play a dominant role, while $A_{x}(s)$ and $A_{y}(s)$ play no role, in spontaneous chiral-symmetry breaking in the DR gauge.

hep-lat↗
arXiv2026

Learning Low Modes of the Wilson Dirac Operator with Gauge-Equivariant Networks

In adaptive multigrid, test vectors that better approximate the low-mode subspace of the Wilson Dirac operator $D$ can reduce the solve time, but their construction can be costly. In some cases, the setup takes longer than a single solve. To reduce the cost of generating test vectors, we train networks built from gauge-equivariant parallel-transport layers once on a quenched ensemble, using a Rayleigh-Ritz loss for $D^\dagger D$. We then test whether the trained networks maintain their performance at other hopping parameters and on configurations not used in training. In these tests, the network outputs are used as test vectors, and the costly $V$-cycle refinement in the adaptive setup is omitted to reduce the setup time. This substantially reduces the setup time while leaving the solve time largely unchanged in most cases. Near the critical hopping parameter $κ_c$, the solve time is also reduced in some cases.

hep-lat↗