Disordered critical wave functions in random-bond models in two dimensions: Random-lattice fermions at without doubling

Abstract

Random-bond Hamiltonians of the (Formula presented) flux state on the square lattice are investigated. It has a special symmetry and all states are paired except the ones with zero energy. Because of this, there are always zero modes. The states near (Formula presented) are described by massless Dirac fermions. For the zero mode, we can construct a random lattice fermion without a doubling and quite large systems (up to (Formula presented) are treated numerically. We clearly demonstrate that the zero mode is given by a critical wave function. Its multifractal behavior is also compared with the effective field theory. © 1997 The American Physical Society.