Ladder approximation to spin velocities in quantum wires

TL;DR

This paper uses the ladder approximation to analyze spin velocities in quantum wires, providing a computationally efficient method that captures key divergences and predicts non-trivial spin conductance consistent with quantum Monte-Carlo data.

Contribution

The study introduces the ladder approximation for spin velocity calculations in quantum wires, capturing logarithmic divergences missed by other methods and enabling efficient analysis of interaction effects.

Findings

Ladder approximation matches QMC data at moderate densities.

Logarithmic divergences are crucial for accurate spin velocity predictions.

LA predicts a non-trivial spin conductance differing from other approximations.

Abstract

The spin sector of charge-spin separated single mode quantum wires is studied, accounting for realistic microscopic electron-electron interactions. We utilize the ladder approximation (LA) to the interaction vertex and exploit thermodynamic relations to obtain spin velocities. Down to not too small carrier densities our results compare well with existing quantum Monte-Carlo (QMC) data. Analyzing second order diagrams we identify logarithmically divergent contributions as crucial which the LA includes but which are missed, for example, by the self-consistent Hartree-Fock approximation. Contrary to other approximations the LA yields a non-trivial spin conductance. Its considerably smaller computational effort compared to numerically exact methods, such as the QMC method, enables us to study overall dependences on interaction parameters. We identify the short distance part of the interaction to govern spin sector properties.