Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

Details Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

1995-09-29

arxiv.org/abs/hep-lat/9509095v2

Nucl.Phys.Proc.Suppl. 47 (1996) 527-534

Physics

High Energy Physics

High Energy Physics - Lattice

Contribution to Lattice 95. 8 pages. Latex source file Individual figures available from chandras@mitlns.mit.edu and also subm

Scientific paper

10.1016/0920-5632(96)00115-6

The QCD phase transition is studied on $16^3$ and $32^3 \times 4$ lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark $\zeta$ and study the resulting chiral condensate, $\azbz$ as a function of the $\zeta$ mass, $m_\zeta$. By examining $\azbz$ for $10^{-10} \le m_\zeta \le 10$ we gain considerable information about the spectrum of Dirac eigenvalues. A comparison of $ma=0.01$ and 0.025 shows little dependence of the Dirac spectrum on such a light, dynamical quark mass, after an overall shift in $\beta$ is removed. The presence of sufficient small eigenvalues to support anomalous chiral symmetry breaking in the high temperature phase is examined quantitatively. In an effort to enhance these small eigenvalues, $\azbz$ is also examined in the pure gauge theory in the region of the deconfinement transition with unexpected results. Above the critical temperature, the three $Z_3$ phases show dramatically different chiral behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a system with one flavor of staggered fermion at $N_t=4$ will possess a chiral a phase transition---behavior not expected in the continuum limit.

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