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=πthis 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>π/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.

8 pages, REVTEX, 3 eps figures, accepted to Phys.Rev.B

References in corpus (3)

• Spin Gap in a Doped Kondo Chain
• Weakly disordered spin ladders
• From the Chern-Simons theory for the fractional quantum Hall effect to the Luttinger model of its edges

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