Quasi-Particle Properties of a One-Dimensional Electron System Interacting with a Short-Range Potential

Abstract

We study the quasi-particle properties of a one-dimensional electron gas interacting via a shortrange electron±electron interaction. The electron self-energy is calculated using the leading-order dynamical-screening approximation with (GWG approximation) and without the vertex corrections (GW approximation). We test the reliability of the plasmon-pole approximation against the full self-energy calculations. Energy relaxation rate via longitudinal optical (LO)-phonon emission is also examined to explore the effects of short-range potential. Our results for the quasi-particle properties indicate that an effective short-range interaction can be used as a qualitative model to understand various quantities in a realistic quantum wire with long-range Coulomb interactions.

Short-range correlations in a one-dimensional electron gas

“…Naturally, there are numerous theoretical investigations dedicated to understanding these effects. [6][7][8][9][10][11][12][13] The exchange and correlation effects describing the screening properties of a system of electrons interacting via the long-range Coulomb interaction potential at high densities is well explained by a mean-field approach: the randomphase approximation ͑RPA͒. However, as the particle density is lowered exchange-correlation effects become important and the RPA fails to explain the physical properties of the system.…”

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

“…Instead we have two points of comparison. First, for a 1D UEG with a contact interaction V(x − x ′ ) = V 0 δ (x − x ′ ), a GW calculation [83] found m * in the range 1 to 2.5 (and presumably continuing to increase), depending on V 0 and the density. These values are comparable to most of our results, ranging between 1 and 5.…”