Related papers: Boundary-bulk relation for topological orders as t…
In this work we present some new understanding of topological order, including three main aspects: (1) It was believed that classifying topological orders corresponds to classifying gapped quantum states. We show that such a statement is…
Organoids are in vitro cellular collectives from which brain-like, or gut-like, or kidney-like structures emerge. To make quantitative predictions regarding the morphology and rheology of a cellular collective in its initial stages of…
In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary manifested by a net of boundary algebras in one dimension lower. This…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
Topology forms a cornerstone in modern condensed matter and statistical physics, offering a new framework to classify the phases and phase transitions beyond the traditional Landau paradigm. However, it is widely believed that topological…
We discuss (2+1)-dimensional gapless surface theories of bulk (3+1)-dimensional topological phases, such as the BF theory at level $\mathrm{K}$, and its generalization. In particular, we put these theories on a flat (2+1) dimensional torus…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. Although it can be treated purely as an algebraic subject, it is inherently topological in nature: the…
In the study of 2d (the space dimension) topological orders, it is well-known that bulk excitations are classified by unitary modular tensor categories. But these categories only describe the local observables on an open 2-disk in the long…
Topos approaches to quantum foundations are described in a unified way by means of spectral bundles, where the base space is a space of contexts and each fibre is its spectrum. Differences in variance are due to the bundle being a fibration…
A finite geometric model of space-time (which we call the bulk) is shown to emerge as a set of error correcting codes. The bulk is encoding a set of messages located in a blow up of the Gibbons-Hoffman-Wootters (GHW) discrete phase space…
We explain how to see finite combinatorics of preorders implicit in the {text} of basic topological definitions or arguments in (Bourbaki, General topology, Ch.I), and define a concise combinatorial notation such that complete definitions…
We propose a new theory to characterize equilibrium topological phase with non-equilibrium quantum dynamics by introducing the concept of high-order topological charges, with novel phenomena being predicted. Through a dimension reduction…
We study a subsector of the AdS_4/CFT_3 correspondence where a class of solutions in the bulk and on the boundary can be explicitly compared. The bulk gravitational theory contains a conformally coupled scalar field with a Phi^4 potential,…
We present explicit mathematical structures that allow for the reconstruction of the field content of a full local conformal field theory from its boundary fields. Our framework is the one of modular tensor categories, without requiring…
We study clustering properties of networks of single integrator nodes over a directed graph, in which the nodes converge to steady-state values. These values define clustering groups of nodes, which depend on interaction topology, edge…
We introduce the concept of a graded bundle which is a natural generalization of the concept of a vector bundle and whose standard examples are higher tangent bundles T^nQ playing a fundamental role in higher order Lagrangian formalisms.…
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…