Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-Andr\'e Model

TL;DR

This paper investigates how barriers to superfluidity and insulation emerge in a 2D Aubry-André model with interacting bosons, revealing the formation of mixed phases and unique phase diagram features due to weakly modulated domains.

Contribution

It introduces a mean-field percolation analysis of the 2D Aubry-André model, highlighting the role of weakly modulated domains in creating mixed phases and complex phase diagrams.

Findings

Barriers to macroscopic phases arise from weakly modulated domains.

Mixed phases dominate the system's properties in certain regimes.

Phase diagrams show lobe-like Bose glass and weak percolation features.

Abstract

We study the ground state phases of interacting bosons in the presence of a 2D Aubry-Andr\'e potential. By using a a mean-field percolation analysis, we focus on several superlattice and quasicrystalline regimes of the 2D Aubry-Andr\'e model, including generalisations that account for a tilting or skewing of the potential. We show that barriers to the onset of macroscopic phases naturally arise from weakly modulated domains in the 2D Aubry-Andr\'e model. This leads to the formation of mixed phases, in which the macroscopic properties are dominated by a minority of the system. The phase diagrams then exhibit substantially different features when compared against crystalline systems, including a lobe-like or wave-like appearance of the Bose glass, sharp extrusions and extended domains with weak percolation. By studying the 2D Aubry-Andr\'e model across multiple regimes, we have shown that the unique properties of mixed phases are not distinct to a small set of parameters.