Related papers: Topological marker in three dimensions based on ke…
We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders - chiral and random types - to explore the interplay between topology and disorder. By tracking…
How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs) which enable the…
We provide a classification of type AII topological quantum systems in dimension d=1,2,3,4. Our analysis is based on the construction of a topological invariant, the FKMM-invariant, which completely classifies "Quaternionic" vector bundles…
We propose a class of models for a magnonic analog of topological insulators in three dimensions. The models have pseudo-time-reversal symmetry which ensures the existence of bosonic Kramers pairs. We define a set of $\mathbb{Z}_2$…
Thin film of superfluid $^3$He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the…
The topological properties of a material depend on its symmetries, parameters, and spatial dimension. Changes in these properties due to parameter and symmetry variations can be understood by computing the corresponding topological…
Topology and disorder have deep connections and a rich combined influence on quantum transport. In order to probe these connections, we synthesized one-dimensional chiral symmetric wires with controllable disorder via spectroscopic…
We consider interface modes in block disordered subwavelength resonator chains in one dimension. Based on the capacitance operator formulation, which provides a first-order approximation of the spectral properties of dimer-type block…
Disorder is ubiquitous in quantum materials, and its interplay with topology can generate phases absent in the clean limit. Using the Haldane model as a minimal setting, we show that disorder not only shifts topological boundaries but also…
Based on previous results of digital topology, this paper focuses on algorithms of topological invariants of objects in 2D and 3D Digital Spaces. We specifically interest in solving hole counting of 2D objects and genus of closed surface in…
Motivated by the recent theoretical and experimental progress in implementing topological orders with photons, we analyze photonic systems with different topologies and present a scheme to probe their topological features. Specifically, we…
Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional…
While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the…
The tensor rank decomposition, also known as canonical polyadic(CP) or simply tensor decomposition, has a long history in multilinear algebra. However, computing a rank decomposition becomes particularly challenging when the rank lies…
Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…
We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the…
We describe nonsymmorphic four-band tight-binding models in one dimension with Kramers degeneracy, and propose topolectric-circuit realizations of their topological phases. We begin with a representative model in the nonsymmorphic AII class…
The investigation of universality questions for local eigenvalue statistics continues to be a driving force in the theory of Random Matrices. For Matrix Models [53] the method of orthogonal polynomials can be used and the asymptotics of the…
In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural…
We introduce a numerical method for identifying topological order in two-dimensional models based on one-dimensional bulk operators. The idea is to identify approximate symmetries supported on thin strips through the bulk that behave as…