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Topological Obstruction in Block-spin Transformations

T. Fujiwara·T. Hayashi·H. Suzuki·K. Wu
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Abstract

Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operators. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables.

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T. Fujiwara, T. Hayashi, H. Suzuki, K. Wu. 2000-06-06. Topological Obstruction in Block-spin Transformations. https://doi.org/10.1016/s0370-2693(00)00920-5

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