Hofstadter butterfly for a finite correlated system

TL;DR

This paper explores how a finite two-dimensional system's energy spectrum and transport properties are affected by magnetic fields, system size, boundary conditions, and Coulomb interactions, revealing the impact of strong correlations on the Hofstadter butterfly.

Contribution

It provides the first analysis of the Hofstadter butterfly's robustness in a finite correlated system, highlighting the influence of Coulomb repulsion on the energy gap under magnetic fields.

Findings

Transport properties depend on system size and parity of the number of sites.

Strong Coulomb repulsion reduces the Hubbard gap with increasing magnetic field.

The Hofstadter butterfly's structure is altered by electronic correlations.

Abstract

We investigate a finite two-dimensional system in the presence of external magnetic field. We discuss how the energy spectrum depends on the system size, boundary conditions and Coulomb repulsion. On one hand, using these results we present the field dependence of the transport properties of a nanosystem. In particular, we demonstrate that these properties depend on whether the system consists of even or odd number of sites. On the other hand, on the basis of exact results obtained for a finite system we investigate whether the Hofstadter butterfly is robust against strong electronic correlations. We show that for sufficiently strong Coulomb repulsion the Hubbard gap decreases when the magnetic field increases.