# Correlated atomic wires on substrates. II. Application to Hubbard wires

## TL;DR

This paper investigates the electronic phases of correlated atomic Hubbard wires on substrates using numerical methods, revealing various localized and delocalized phases and assessing the accuracy of effective ladder models.

## Contribution

It applies and validates effective ladder models to study correlated Hubbard wires on substrates, providing insights into phase behavior and model accuracy.

## Key findings

- Identification of paramagnetic Mott insulators, Luttinger liquids, and Heisenberg chains.
- Effective ladder models accurately reproduce low-energy excitations.
- Qualitative predictions of localization/delocalization of excitations.

## Abstract

In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-$1/2$ Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.