Flat-band (de)localization emulated with a superconducting qubit array

TL;DR

This paper demonstrates how a superconducting qubit array can emulate a rhombic lattice with flat bands, revealing disorder-induced localization and delocalization phenomena, and observing a quantum critical transition.

Contribution

It introduces a superconducting qubit array platform to simulate flat-band physics and studies the interplay of disorder and localization in this system.

Findings

Disorder induces localization in dispersive bands.

Disorder causes delocalization in flat bands.

A sharp transition and quantum critical scaling are observed.

Abstract

Arrays of coupled superconducting qubits are analog quantum simulators able to emulate a wide range of tight-binding models in parameter regimes that are difficult to access or adjust in natural materials. In this work, we use a superconducting qubit array to emulate a tight-binding model on the rhombic lattice, which features flat bands. Enabled by broad adjustability of the dispersion of the energy bands and of on-site disorder, we examine regimes where flat-band localization and Anderson localization compete. We observe disorder-induced localization for dispersive bands and disorder-induced delocalization for flat bands. Remarkably, we find a sudden transition between the two regimes and, in its vicinity, the semblance of quantum critical scaling.