Related papers: Crystallography of Hyperbolic Lattices
A hyperbolic lattice allows for any $p$-fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only twofold, threefold, fourfold or sixfold rotational symmetry is permitted. This unique feature…
A systematic framework for realizing $\mathbb{Z}_2$ gauge extensions of hyperbolic lattices within the nearest-neighbor tight-binding formalism is developed. Using the triangle group $\Delta(2,8,8)$ as an example, we classify all…
Hyperbolic lattices present a unique opportunity to venture beyond the conventional paradigm of crystalline many-body physics and explore correlated phenomena in negatively curved space. As a theoretical benchmark for such investigations,…
We study tight-binding models in the crossover from hyperbolic to Euclidean lattices, realized through the successive insertion of Euclidean defects into hyperbolic lattices. We analyze how the holographic two-point boundary correlation…
The terms of topological and quantum stabilities of low-dimensional crystalline carbon lattices with multiple non-equivalent sublattices are coined using theoretical analysis, multilevel simulations, and available experimental structural…
Topological band theory establishes a standardized framework for classifying different types of topological matters. Recent investigations have shown that hyperbolic lattices in non-Euclidean space can also be characterized by hyperbolic…
Topological flat bands (TFBs) provide a promising platform to investigate intriguing fractionalization phenomena, such as the fractional Chern insulators (FCIs). Most of TFB models are established in two-dimensional Euclidean lattices with…
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…
We investigate the dynamic properties of elastic lattices defined by tessellations of a curved hyperbolic space. The lattices are obtained by projecting nodes of a regular hyperbolic tessellation onto a flat disk and then connecting those…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…
After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. Lattices of superconducting coplanar waveguide (CPW) resonators have been…
Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices…
Motivated by recent theoretical and experimental developments in the physics of hyperbolic crystals, we study the noncommutative Bloch transform of Fuchsian groups that we call the hyperbolic Bloch transform. First, we prove that the…
Recent breakthroughs in hyperbolic lattices have expanded the study of topological phases of matter from Euclidean to non-Euclidean spaces. However, prior work has mostly focused on spatial topological states at the single outer edge of…
Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…
The band structure of a crystal may have points where two or more bands are degenerate in energy and where the geometry of the Bloch state manifold is singular, with consequences for material and transport properties. Ultracold atoms in…
The origin of many quantum-material phenomena is intimately related to the presence of flat electronic bands. In quantum simulation, such bands have been realized through line-graph lattices, a class of lattices known to exhibit flat bands.…
Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal…
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…