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

Yasuhiro Hatsugai·Xiao-Gang Wen·Mahito Kohmoto
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Abstract

Random bond Hamiltonians of the $π$ 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.

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Yasuhiro Hatsugai, Xiao-Gang Wen, Mahito Kohmoto. 1996-03-27. Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at $E=0$ without Doubling. https://doi.org/10.1103/physrevb.56.1061

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