1998/03/30 by D. N. Aristov
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.57.12825
published as PRB 57, 12825 (1998) · 8 pages, REVTEX, 3 eps figures, accepted to Phys.Rev.B
arxiv created 1998/03/30 · openalex publication_date 1998/05/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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=\ensuremathπ this exponential is associated with the Wigner-Jordan transformation in 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>\ensuremathπ/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.