Correlations in the impenetrable electron gas

Frank Göhmann, Alexander Rudol'fovich Its, V. E. Korepin, Department Of Mathematical Sciences

Published Jan 1, 1998• 11 citations

Abstract

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

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Correlations in the impenetrable electron gas

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Published Jan 1, 1998• 11 citations

OpenAlex

Abstract

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κ\to 1

and

κ\to 0

, of the statistics parameter

κ

, and coincide with the predictions of the conformal field theory at low temperatures.

n(k)

at zero temperature does not present algebraic singularities but the tails obey the universal decay ${lim}_{k\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}}n(k)\ensuremath{\sim}C/{k}^{4}$ with the amplitude

C

given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.