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Disordered Dirac Fermions: Multifractality Termination and Logarithmic Conformal Field Theories
We reexamine in detail the problem of fermions interacting with a non-Abelian
random vector potential. Without resorting to the replica or supersymmetry
approaches, we show that in the limit of infinite disorder strength the theory
possesses an exact solution which takes the form of a logarithmic conformal
field theory. We show that the proper treatment of the locality conditions in
the SU(2) theory leads to the termination of the multifractal spectrum, or in
other words to the termination of the infinite hierarchies of
negative-dimensional operators that were thought to occur. Based on arguments
of logarithmic degeneracies, we conjecture that such a termination mechanism
should be present for general SU(N). Moreover, our results lead to the
conclusion that the previous replica solution of this problem yields incorrect
results.Comment: Revised version, to appear in Nucl. Phys.