Bosonization of the interacting Su-Schrieffer-Heeger model

TL;DR

This paper develops a bosonization approach for the interacting SSH model with open boundaries, enabling analytical predictions of Majorana edge mode localization affected by interactions and staggering.

Contribution

It introduces a bosonization method for the interacting SSH model and analyzes how interactions influence edge mode localization depending on system parameters.

Findings

Bosonization accurately predicts Majorana edge mode density profiles.

Interactions do not universally localize or delocalize edge modes.

Localization length varies with interaction strength and staggering parameter.

Abstract

We derive the bosonization of the interacting fermionic Su-Schrieffer-Heeger (SSH) with open boundaries. We use the classical Euler-Lagrange equations of motions of the bosonized theory to compute the density profile of the Majorana edge mode and observe excellent agreement with numerical results, notably the localization of the mode near the boundaries. Remarkably, we find that repulsive or attractive interactions do not systematically localize or delocalize the edge mode but their effects depend on the value of the staggering parameter. We provide quantitative predictions of these effects on the localization length of the edge mode.