# Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction

## TL;DR

This paper explores how strong electron interactions influence the spectral properties and phase stability of quantum wires with significant Rashba spin-orbit coupling and magnetic fields, revealing enhanced topological phases and exotic excitations.

## Contribution

It combines Matrix Product State and bosonization techniques to analyze a microscopic extended Hubbard model, uncovering interaction effects on spectral gaps and optical conductivity.

## Key findings

- Interactions increase the pseudo gap at k=0.
- Interactions enhance the Majorana-supporting phase.
- Optical conductivity is dominated by breather states.

## Abstract

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at $k = 0$ and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.