Some results in the theory of interacting electron systems

R. F. Bishop

Asgari Reza

This review article is about the role of electron-electron interactions in low dimensional systems and its transport properties in nano-structures. It begins with a review of the pair-distribution function theory of electron liquid systems taking into account the electron-electron interactions. We extend the theory for highly correlated system such two- and one-dimensional electron liquids. We then review the microscopic theory of the local-field factors and calculate the quasiparticle properties in two-dimension electron liquid and compare our results with those measured by recent experiments. The physics of two-dimension bilayer structures are revised and are immediately applied to the study of charged Coulomb drag effects in a bilayer electron-electron system and results are compared with experimental data. As a final application, the Luttinger theory is discussed and we compare our recent calculations with those obtained from quantum Monte Carlo simulation for one dimensional electron liquid.

Philippe Nozières

Michael Seidl

Two interacting electrons that are confined to the surface of a sphere have a uniform ground-state (surface) density. The Schr\"odinger equation of this helium-type two-electron system is solved here accurately for different values $\ensuremath{\alpha}∊\mathbb{R}$ of a constant that is multiplied to the electron-electron repulsion ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{V}}_{\mathit{ee}}$. The correlation structure in the resulting wave functions is analyzed for different values of $\ensuremath{\alpha}$. The asymptotic limits $\ensuremath{\alpha}\ensuremath{\rightarrow}0$ and $\ensuremath{\alpha}\ensuremath{\rightarrow}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$ are treated analytically. Using these results, the ISI (interaction-strength interpolation) model for the density-functional ${E}_{\mathit{xc}}[\ensuremath{\rho}]$ of the exchange-correlation energy in the real system with $\ensuremath{\alpha}=1$ is tested against the exact adiabatic connection in density-functional theory.

Ph. Nozières, Daniel W. Hone, M. E. Rose

Steven Allan Kivelson, H. B. Thacker, Weikang Wu

We consider the effects of repulsive electron-electron interactions between electrons of like spin in conducting polymers. Because the ratio W/2m of the physical bandwidth W to the band gap 2m is large in these systems, they may be represented by a field-theory model with a cutoff. When only interactions between like spins are included, the resulting model is equivalent to the massive Thirring model which has been exactly solved by Bethe's ansatz. From the exact solution we are able to conclude that perturbation theory in the interaction strength g is quite accurate so long as (g/\ensuremath{\pi})ln(W/2m)\ensuremath{\ll}1, while renormalization-group-improved perturbation theory is valid for (g/\ensuremath{\pi})\ensuremath{\ll}1. For (g/\ensuremath{\pi})\ensuremath{\gtrsim}1, results for the ground-state energy and mass gap are sensitive to the band structure far from the Fermi surface, and no simple field-theory model is adequate.