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Progress of Theoretical Physics

One-Dimensional Electron Gas with Delta-Function Interaction at Finite Temperature

Minoru Takahashi

Published Nov 1, 1971• 105 citations
Publisher

Abstract

Integral equations which describe the thermodynamic properties of a one-dimensional electron gas with repulsive and attractive delta-function interactions are obtained. From these equations one can calculate the energy, entropy, magnetization, particle density and pressure at given temperature, magnetic field and chemical potential.
DOI
10.1143/ptp.46.1388

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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.