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.
@article{arxiv.2410.07878,
title = {Flat-band (de)localization emulated with a superconducting qubit array},
author = {Ilan T. Rosen and Sarah Muschinske and Cora N. Barrett and David A. Rower and Rabindra Das and David K. Kim and Bethany M. Niedzielski and Meghan Schuldt and Kyle Serniak and Mollie E. Schwartz and Jonilyn L. Yoder and Jeffrey A. Grover and William D. Oliver},
journal= {arXiv preprint arXiv:2410.07878},
year = {2025}
}