We study Anderson localization in disordered tight-binding models on hyperbolic lattices.
Such lattices are geometries intermediate between ordinary two-dimensional crystalline …

We extend the notion of topologically protected semi-metallic band crossings to hyperbolic
lattices in a negatively curved plane. Because of their distinct translation group structure …

Wave functions on periodic lattices are commonly described by Bloch band theory. Besides
Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian …

Particles hopping on a two-dimensional hyperbolic lattice feature unconventional energy
spectra and wave functions that provide a largely uncharted platform for topological phases …

We study the energy spectrum of tight-binding Hamiltonians for regular hyperbolic tilings.
More specifically, we compute the density of states using the continued-fraction expansion of …

Tessellations of the hyperbolic spaces by regular polygons support discrete quantum and
classical models with unique spectral and topological characteristics. Resolving the true …

Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum
electrodynamics and electric-circuit networks, where particles coherently hop on a discrete …

We establish a connection between the electromagnetic Hall response and band topological
invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless …

Hyperbolic lattices present a unique opportunity to venture beyond the conventional
paradigm of crystalline many-body physics and explore correlated phenomena in negatively …

We consider synthetic materials consisting of self-coupled identical resonators carrying
classical internal degrees of freedom. The architecture of such material is specified by the …