Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling

Abstract

Random bond Hamiltonians of the $\pi$ 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 $E=0$ 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 $801\times 801$) 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.

4 pages, 2 postscript figures

References in corpus (4)

• Scaling Theory of the Integer Quantum Hall Effect
• Disorder Effects in Two-Dimensional d-wave Superconductors
• Two-dimensional conformal field theory for disordered systems at criticality
• Gaussian field theories, random Cantor sets and multifractality

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