Interaction-range effects for fermions in one dimension

TL;DR

This study investigates how the range of electron-electron interactions affects the physical properties of one-dimensional fermionic systems, revealing a transition from spin to charge dominance and robust spin-charge separation.

Contribution

It provides a detailed analysis of the impact of interaction range on Luttinger liquid parameters and phase transitions in 1D fermionic chains using quantum Monte Carlo and exact diagonalization.

Findings

K_rho decreases with increasing interaction range

Metal-insulator transition occurs at K_rho=1/4

Charge and spin correlations show crossover with screening length

Abstract

Experiments on quasi-one-dimensional systems such as quantum wires and metallic chains on surfaces suggest the existence of electron-electron interactions of substantial range and hence physics beyond the Hubbard model. We therefore investigate one-dimensional, quarter-filled chains with a Coulomb potential with variable screening length by quantum Monte Carlo methods and exact diagonalization. The Luttinger liquid interaction parameter K_rho decreases with increasing interaction strength and range. Experimentally observed values close to 1/4 require strong interactions and/or large screening lengths. As predicted by bosonization, we find a metal-insulator transition at K_rho=1/4. Upon increasing the screening length, the charge and spin correlation functions reveal the crossover from dominant 2k_F spin correlations to dominant 4k_F charge correlations, and a strong enhancement of the charge velocity. In the metallic phase, the signatures of spin-charge separation in the single-particle spectrum, spinon and holon bands, remain robust even for rather long-ranged interactions. The charge-density-wave state exhibits backfolded shadow bands.