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Quantum fluctuations of one-dimensional free fermions and Fisher-Hartwig formula for Toeplitz determinants | Alexander G. Abanov
; Dmitri A. Ivanov
; Yachao Qian
; | Date: |
5 Aug 2011 | Abstract: | We revisit the problem of finding the probability distribution of a fermionic
number of one-dimensional spinless free fermions on a segment of a given
length. The generating function for this probability distribution can be
expressed as a determinant of a Toeplitz matrix. We use the recently proven
generalized Fisher--Hartwig conjecture on the asymptotic behavior of such
determinants to find the generating function for the full counting statistics
of fermions on a line segment. Unlike the method of bosonization, the
Fisher--Hartwig formula correctly takes into account the discreteness of
charge. Furthermore, we check numerically the precision of the generalized
Fisher--Hartwig formula, find that it has a higher precision than rigorously
proven so far, and conjecture the form of the next-order correction to the
existing formula. | Source: | arXiv, 1108.1355 | Services: | Forum | Review | PDF | Favorites |
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