Dirac Fermions on a Two-Dimensional Lattice and the Intermediate Metallic Phase

Abstract

Consequences of different discretizations of the two-dimensional Dirac operator on low energy properties (e.g., the number of nodes) and their relations to gauge properties are discussed. Breaking of the gauge invariance was suggested in a recent work by M. Bocquet, D. Serban, and M.R. Zirnbauer [cond-mat/9910480] in order to destroy an intermediate metallic phase of lattice Dirac fermions with random mass. It is explained that such a procedure is inconsistent with the underlying lattice physics. Previous results point out that the logarithmic growth of the slope of the average density of states with the system size, obtained in the field-theoretical calculation of M. Bocquet et al., could be a precursor for the appearence of an intermediate metallic phase.