A one-to-two dimensional mapping using a partial fast Fourier transform

Details A one-to-two dimensional mapping using a partial fast Fourier transform A one-to-two dimensional mapping using a partial fast Fourier transform

2011-06-28

arxiv.org/abs/1106.5663v1

Physica A, Volume 389, Issue 15, p. 2939-2944. (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

It will be shown how to map a simple one-dimensional tight binding model with a cosine potential in one dimension exactly to a two dimensional tight binding model with periodic boundary conditions with the presence of a single flux quantum spread evenly on the torus. The mapping is is achieved by a partial sequence of "Fast Fourier Transform" (FFT) steps which if completed would be an exact Fourier transform of the original model. Each step of the FFT recursively maps a tight binding model into two decoupled sublattices of half the lattice length.

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