Universal correlations of one-dimensional electrons at low density

Details Universal correlations of one-dimensional electrons at low density Universal correlations of one-dimensional electrons at low density

2000-07-20

arxiv.org/abs/cond-mat/0007327v1

Physics

Condensed Matter

22 pages, AMS-Latex, invited talk, presented at the workshop on `Isomonodromic Deformations and Applications in Physics', Mont

Scientific paper

We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension. Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid. Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons. This model, which we call the impenetrable electron gas, allows for a rigorous mathematical treatment. In particular, a so-called determinant representation for the two particle Green function could be derived. This determinant representation is related to an integrable classical evolution equation and to a Riemann-Hilbert problem, that enable the exact calculation of the asymptotics of the two-particle Green functions.

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