相关论文: Boundary-bulk relation for topological orders as t…

We investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization. We also show that topological realization of…

It was shown recently, building on work of Alexakis, Balehowksy, and Nachman that the geometry of (some portion of) a manifold with boundary is uniquely fixed by the areas of a foliation of two-dimensional disk-shaped surfaces anchored to…

We consider a few types of bounded homomorphisms on a topological group. These classes of bounded homomorphisms are, in a sense, weaker than the class of continuous homomorphisms. We show that with appropriate topologies each class of these…

The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose…

It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…

The classification of rational conformal field theories is reconsidered from the standpoint of boundary conditions. Solving Cardy's equation expressing the consistency condition on a cylinder is equivalent to finding integer valued…

The Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulae suggest that bulk geometry emerges from the entanglement structure of the boundary theory. Using these formulae, we build on a result of Alexakis, Balehowsky, and Nachman to show…

The relationship between bulk and boundary properties is one of the founding features of (Rational) Conformal Field Theory. Our goal in this paper is to explore the possibility of having an equivalent relationship in the context of lattice…

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…

We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge…

Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…

In this thesis we propose and study a theory of ordered locales, a type of point-free space equipped with a preorder structure on its frame of opens. It is proved that the Stone-type duality between topological spaces and locales lifts to a…

In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.

A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…

Topological materials are renowned for their ability to harbor states localized at their peripheries, such as surfaces, edges, and corners. Accompanying these states, fractional charges appear on peripheral unit cells. Recently,…

Topological quantum error correction based on the manipulation of the anyonic defects constitutes one of the most promising frameworks towards realizing fault-tolerant quantum devices. Hence, it is crucial to understand how these defects…

We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…

AdS/CFT correspondence gives us a bulk-boundary dictionary between CFT operators and local fields in the bulk. Can a bulk-boundary dictionary exist for a non local bulk field? In this paper we consider a particular non local theory and show…

The bulk-boundary correspondence, which links a bulk topological property of a material to the existence of robust boundary states, is a hallmark of topological insulators. However, in crystalline topological materials the presence of…