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arXiv:cond-mat/9809076 · Physics Letters A

Correlations in the impenetrable electron gas

F. Göhmann, Alexander Rudol'fovich Its, V.E. Korepin

Published Nov 1, 1998• 18 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(98)00711-7

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We consider non-relativistic electrons in one dimension with infinitely strong repulsive delta function interaction. We calculate the long-time, large-distance asymptotics of field-field correlators in the gas phase. The gas phase at low temperatures is characterized by the ideal gas law. We calculate the exponential decay, the power law corrections and the constant factor of the asymptotics. Our results are valid at any temperature. They simplify at low temperatures, where they are easily recognized as products of free fermionic correlation functions with corrections arising due to the interaction. PACS: 05.30.Fk; 71.10.Pm; 71.27.+a
We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.