Site-selective correlations in interacting "flat-band" quasicrystals

TL;DR

This study uses quantum Monte Carlo simulations to explore how onsite repulsion affects quasicrystals with flat-band signatures, revealing site-dependent correlations linked to local coordination.

Contribution

It demonstrates site-selective correlation effects in interacting quasicrystals, highlighting the role of local coordination in flat-band systems.

Findings

Sites with lower coordination are more affected by interactions.

Global properties like the Mott transition are similar to periodic lattices.

Local density of states varies with site coordination.

Abstract

Model lattices such as the kagome and Lieb lattices have been widely investigated to elucidate the properties of interacting flat-band systems. While a quasicrystal does not have proper bands, the non-interacting density of states of several of them displays the typical signature of a flat band pinned at the Fermi level: a delta-function zero-energy peak. Here, we employ quantum Monte Carlo simulations to determine the effect of onsite repulsion on these quasicrystals. While global properties such as the antiferromagnetic structure factor and the specific heat behave similarly as in the case of periodic lattices undergoing a Mott transition, the behavior of the local density of states depends on the coordination number of the site. In particular, sites with the smallest coordination number, which give the dominant spectral-weight contribution to the zero-energy peak, are the ones most strongly impacted by the interaction. Besides establishing site-selective correlations in quasicrystals, our work also points to the importance of the real-space structure of flat bands in interacting systems.