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28 March 2024
 
  » arxiv » 1108.1355

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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
AbstractWe 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
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