Related papers: Reduced Wannier representation for topological ban…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…
We consider a real periodic Schr\"odinger operator and a physically relevant family of $m \geq 1$ Bloch bands, separated by a gap from the rest of the spectrum, and we investigate the localization properties of the corresponding composite…
Topological insulators are well-known for their topological edge states, which are protected by the non-trivial bulk topology and characterized by gapless Wannier bands, a phenomenon known as the bulk-boundary correspondence. However,…
Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…
Topological flat bands, such as the band in twisted bilayer graphene, are becoming a promising platform to study topics such as correlation physics, superconductivity, and transport. In this work, we introduce a generic approach to…
Autoencoders represent an effective approach for computing the underlying factors characterizing datasets of different types. The latent representation of autoencoders have been studied in the context of enabling interpolation between data…
We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are…
Maximally-localized Wannier functions (MLWFs) are widely employed as an essential tool for calculating the physical properties of materials due to their localized nature and computational efficiency. Projectability-disentangled Wannier…
Topological lasers, known for their robustness and unique features originating from nontrivial topology, have recently become a focal point of research in photonics. In this work, we propose a topological laser based on two-dimensional…
Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in…
Hyperspectral image analysis often requires selecting the most informative bands instead of processing the whole data without losing the key information. Existing band reduction (BR) methods have the capability to reveal the nonlinear…
The systematic diagnosis of band topology enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing…
In this paper we study the formation of topological Tamm states at the interface between a semi-infinite one-dimensional photonic-crystal and a metal. We show that when the system is topologically non-trivial there is a single Tamm state in…
Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…
Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…
Nontrivial quantum geometry of electronic bands has been argued to facilitate superconductivity even for the case of flat dispersions where the conventional contribution to the superfluid weight is suppressed by the large effective mass.…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…