Higher-dimensional Euclidean and non-Euclidean structures in planar circuit quantum electrodynamics

TL;DR

This paper extends the simulation of planar hyperbolic lattices in circuit quantum electrodynamics to higher-dimensional Euclidean and non-Euclidean lattices, revealing complex spectra with flat bands and frustration.

Contribution

It introduces a method to realize higher-dimensional lattice structures in circuit QED, broadening the scope of non-Euclidean geometries accessible with current technology.

Findings

Effective Hamiltonians correspond to higher-dimensional Kagomé-like structures.

Derived an exact expression for the fraction of flat-band states.

Analyzed spectra showing strong frustration and flat bands.

Abstract

We show that a recent proposal for simulating planar hyperbolic lattices with circuit quantum electrodynamics can be extended to accommodate also higher dimensional lattices in Euclidean and non-Euclidean spaces if one allows for circuits with more than three polygons at each vertex. The quantum dynamics of these circuits, which can be constructed with present-day technology, are governed by effective tight-binding Hamiltonians corresponding to higher-dimensional Kagom\'{e}-like structures ($n$-dimensional zeolites), which are well known to exhibit strong frustration and flat bands. We analyze the relevant spectra of these systems and derive an exact expression for the fraction of flat-band states. Our results expand considerably the range of non-Euclidean geometry realizations with circuit quantum electrodynamics.