Superconducting circuit simulator of Bose-Hubbard model with a flat band

TL;DR

This paper explores a superconducting circuit-based quantum simulator for the Bose-Hubbard model on a flat-band saw-tooth lattice, revealing localization phenomena, phase transitions, and interaction effects relevant for quantum many-body physics.

Contribution

It introduces a superconducting circuit design for simulating the Bose-Hubbard model with flat bands, analyzing localization, phase transitions, and interaction effects in this setup.

Findings

Localization-delocalization transition with sign change of hopping

Localized density patterns in strongly attractive interactions

Two-particle correlations distinguish interaction regimes

Abstract

Recent advance in quantum simulations of interacting photons using superconducting circuits offers opportunities for investigating the Bose-Hubbard model in various geometries with hopping coefficients and self-interactions tuned to both signs. Here we investigate phenomena related to localized states associated with a flat-band supported by the saw-tooth geometry. A localization-delocalization transition emerges in the non-interacting regime as the sign of hopping coefficient is changed. In the presence of interactions, patterns of localized states approach a uniform density distribution for repulsive interactions while interesting localized density patterns can arise in strongly attractive regime. The density patterns indicate the underlying inhomogeneity of the simulator. Two-particle correlations can further distinguish the nature of the localized states in attractive and repulsive interaction regimes. We also survey possible experimental implementations of the simulator.