A Luttinger Liquid in Box

TL;DR

This paper investigates how electron wave-functions in a finite one-dimensional wire with interactions differ from non-interacting cases, revealing edge depletions and spin-charge separation effects in a Luttinger Liquid.

Contribution

It provides a detailed analysis of the local spectral weight and wave-function structure in a finite Luttinger Liquid with boundary conditions, highlighting interaction effects.

Findings

Edge depletion of spectral weight near boundaries

Modulations indicating spin-charge separation

Interaction-induced structure in wave-functions

Abstract

We study a Luttinger Liquid in a finite one-dimensional wire with box-like boundary conditions by considering the local distribution of the single particle spectral weight. This corresponds to the experimental probability of extracting a single electron at a given place and energy, which can be interpreted as the square of an electron wave-function. For the non-interacting case, this is given by a standing wave at the Fermi wave-vector. In the presence of interactions, however, the wave-functions obtain additional structure with a sharp depletion near the edges and modulations throughout the wire. In the spinful case, these modulations correspond to the separate spin- and charge-like excitations in the system.