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Using the Dirac-mode expansion method, which keeps the gauge invariance, weanalyze the Polyakov loop in terms of the Dirac modes in SU(3) quenched latticeQCD in both confined and deconfined phases. First, to investigate the directcorrespondence between confinement and chiral symmetry breaking, we removelow-lying Dirac-modes from the confined vacuum generated by lattice QCD. Inthis system without low-lying Dirac modes, while the chiral condensate $\langle\bar{q} q\rangle$ is extremely reduced, we find that the Polyakov loop isalmost zero and $Z_3$-center symmetry is unbroken, which indicates quarkconfinement. We also investigate the removal of ultraviolet (UV) Dirac-modes,and find that the Polyakov loop is almost zero. Second, we deal with thedeconfined phase above $T_c$, and find that the behaviors of the Polyakov loopand $Z_3$-symmetry are not changed without low-lying or UV Dirac-modes.Finally, we develop a new method to remove low-lying Dirac modes from thePolyakov loop for a larger lattice of $12^3 \times 4$ at finite temperature,and find almost the same results. These results suggest that each eigenmode hasthe information of confinement, i.e., the "seed" of confinement is distributedin a wider region of the Dirac eigenmodes unlike chiral symmetry breaking, andthere is no direct correspondence between confinement and chiral symmetrybreaking through Dirac-eigenmodes.

Lattice QCD analysis of the Polyakov loop in terms of Dirac eigenmodes