Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
1998-03-30
PRB 57, 12825 (1998)
Physics
Condensed Matter
Strongly Correlated Electrons
8 pages, REVTEX, 3 eps figures, accepted to Phys.Rev.B
Scientific paper
10.1103/PhysRevB.57.12825
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.
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