Boundary Green's Function for Spin-Incoherent Interacting Electrons in One Dimension

TL;DR

This paper develops a bosonization approach for spin-incoherent one-dimensional electrons with boundaries, predicting oscillations in tunneling conductance that reveal charge excitation properties and interaction strength.

Contribution

It introduces a bosonization scheme for strongly interacting electrons with boundaries, enabling analysis of boundary effects on charge correlations in the spin-incoherent regime.

Findings

Charge sector exhibits boundary-sensitive power-law scaling.

Predicted oscillations in tunneling conductance depend on charge excitation velocity.

The approach describes crossover between boundary and bulk regimes.

Abstract

The spin-incoherent regime of one-dimensional electrons has recently been explored using the Bethe ansatz and a bosonized path integral approach, revealing that the spin incoherence dramatically influences the correlations of charge excitations. We here introduce a bosonization scheme for strongly interacting electrons, allowing us to generalize the description to account for the presence of an open boundary. By calculating the single-electron Green's function we find that the charge sector power-law scaling is highly sensitive to the boundary. Our result allows for a detailed description of the crossover between boundary and bulk regimes. We predict that scanning tunneling microscopy on a spin-incoherent system will pick up oscillations in the differential tunneling conductance as a function of the applied voltage $V$ at "intermediate" distances $x$ from a real or a dynamically generated boundary. The wavelength of the oscillations, $\pi v_c/x$, probes the speed $v_c$ of the charge excitations, and therefore the strength of the electron-electron interaction.