Is the chiral phase transition induced by a metal-insulator transition?

Abstract

We investigate the QCD Dirac operator with gauge configurations given by a liquid of instantons in the region of temperatures about the chiral phase transition. Both the quenched and unquenched cases are examined in detail. We present evidence of a localization transition in the low lying modes of the Dirac operator around the same temperature as the chiral phase transition. Thus both level statistics and eigenvectors of the QCD Dirac operator at the chiral phase transition have similar properties than those of a disordered conductor at the metal-insulator transition. This strongly suggests the phenomenon of Anderson localization (localization by destructive quantum interference) is the leading physical mechanism in the restoration of the chiral symmetry. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.

Burgers-like equation for spontaneous breakdown of the chiral symmetry in QCD

“…As far as we know, the microscopic spectral density at criticality was constructed explicitly only for b = N f + |ν| = 0 case [30], and was never checked by the lattice simulation. Taking into account the still ongoing discussion on the nature of chiral phase transition, its relation to confinement and Anderson localization [31,32], lattice verification of analytic predictions for microscopic densities at the critical point may be a powerful tool to shed more light on this aspect of strong interactions.…”