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arXiv:cond-mat/9803365 · Physical review. B, Condensed matter

Bosonization for a Wigner-Jordan-like transformation: Backscattering and umklapp processes on a fictitious lattice

D. N. Aristov

Published May 15, 1998• 11 citations
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Abstract

We analyze the asymptotic behavior of the exponential form in the fermionic density operators as a function of ruling parameter $Q$. In the particular case $Q=\ensuremath{\pi}$ this exponential is associated with the Wigner-Jordan transformation in $\mathrm{XY}$ spin chain model. We compare the bosonization approach and the evaluation using the Toeplitz determinant. In the latter method, the Szeg\"o-Kac theorem suggests that at $Q>\ensuremath{\pi}/3$ a bosonized solution is accompanied by a faster decaying one. The second solution is revealed as an umklapp process on the fictitious lattice, and originates from backscattering terms in the bosonized density. Our finding remains true in a wide range of fermion filling ratios.

DOI
10.1103/physrevb.57.12825

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