Related papers: Linking confinement to spectral properties of the …
We represent the Polyakov loop correlator as a spectral sum of correlators of eigenvectors of the lattice Dirac operator. This spectral representation is studied numerically using quenched SU(3) configurations below and above the…
We compute complete spectra of the staggered lattice Dirac operator for quenched SU(3) gauge configurations below and above the critical temperature. The confined and the deconfined phase are characterized by a different response of the…
Aiming at the link between confinement and chiral symmetry the Polyakov loop represented as a spectral sum of eigenvalues of the Dirac operator was subject of recent studies. We analyze the volume dependence as well as the continuum…
We study interplay between confinement/deconfinement and chiral properties. We derive some analytical relations of the Dirac modes with the confinement quantities, such as the Polyakov loop, its susceptibility and the string tension. For…
We investigate correlations of the Polyakov loop fluctuations with eigenmodes of the lattice Dirac operator. Their analytic relations are derived on the temporally odd-number size lattice with the normal non-twisted periodic boundary…
Dirac spectrum representations of the Polyakov loop fluctuations are derived on the temporally odd-number lattice, where the temporal length is odd with the periodic boundary condition. We investigate the Polyakov loop fluctuations based on…
We study the localization properties of the eigenmodes of the staggered Dirac operator across the deconfinement transition in finite-temperature $\mathbb{Z}_3$ pure gauge theory on the lattice in 2+1 dimensions. This allows for nontrivial…
Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov loop are thoroughly investigated. The approach by Gattringer is generalized to mode sums which reconstruct the Polyakov loop locally. This opens the possibility…
In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the Dirac eigenvalues $\lambda_n$ in QCD, i.e., $\langle L_P \rangle \propto \sum_n \lambda_n^{N_t -1} \langle…
We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…
The Polyakov loop and the Dirac modes are connected via a simple analytical relation on the temporally odd-number lattice, where the temporal lattice size is odd with the normal (nontwisted) periodic boundary condition. Using this relation,…
In the lattice QCD formalism, we investigate the relation between confinement and chiral symmetry breaking. A gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes is derived on a temporally odd-number…
We study the localization properties of the eigenmodes of the staggered Dirac operator in finite-temperature $\mathbb{Z}_2$ pure gauge theory on the lattice in 2+1 dimensions. We find that the low modes turn from delocalized to localized as…
We study the relation between quark confinement and spontaneous chiral-symmetry breaking directly in QCD. In lattice QCD formalism, we derive an analytical gauge-invariant relation between the Polyakov loop $\langle L_P \rangle$ and the…
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop,…
Inspired by the fact that both the dilaton potential encoding the trace anomalies of QCD and the Polyakov loop potential measuring the deconfinement phase transition can be expressed in the logarithmic forms, as well as the fact that the…
We investigate and compute spectral sums of the Wilson lattice Dirac operator for quenched SU(3) gauge theory. It is demonstrated that there exist sums which serve as order parameters for the confinement-deconfinement phase transition and…
In the lattice QCD formalism, we derive a gauge-invariant analytical relation connecting the Polyakov loop and the Dirac modes on a temporally odd-number lattice, where the temporal lattice size is odd, with the normal (nontwisted) periodic…
To clarify the relation between confinement and chiral symmetry breaking in QCD, we consider a temporally odd-number lattice, with the temporal lattice size $N_t$ being odd. We here use an ordinary square lattice with the normal…
We study quark confinement by computing the Polyakov loop potential in Yang--Mills theory within different non-perturbative functional continuum approaches [1]. We extend previous studies in the formalism of the functional renormalisation…