Bosonization for Wigner-Jordan-like Transformation : Backscattering and Umklapp-processes on Fictitious Lattice
Abstract
We analyze the asymptotic behavior of the exponential form in the fermionic density operators as the function of ruling parameter Q. In the particular case Q=\pi this exponential associates with the Wigner-Jordan transformation for XY spin chain model. We compare the bosonization approach and the evaluation via the Toeplitz determinant. The use of Szego-Kac theorem suggests that at Q>\pi/3 the divergent series for intrinsic logarithm provides a bosonized solution and faster decaying one, found as the logarithm's value on another sheet of the complex plane. The second solution is revealed as umklapp-process on the fictitious lattice while originates from backscattering terms in bosonized density. Our finding preserves in a wide range of fermion filling ratios.
Keywords
Cite
@article{arxiv.cond-mat/9803365,
title = {Bosonization for Wigner-Jordan-like Transformation : Backscattering and Umklapp-processes on Fictitious Lattice},
author = {D. N. Aristov},
journal= {arXiv preprint arXiv:cond-mat/9803365},
year = {2009}
}
Comments
8 pages, REVTEX, 3 eps figures, accepted to Phys.Rev.B