Related papers: Computing Defects Associated to Bounded Domain Wal…
We demonstrate how to do many computations for non-chiral topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects. Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate…
This paper introduces a novel systematic construction of gapped domain walls (GDWs) within the Levin-Wen (LW) model. By gluing two LW models along their open sides in a compatible way, we achieve a complete GDW classification by subsets of…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer-Picard ring for the fusion category…
A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the constraint domain into hyperrectangular subcells until the…
We explore the idea of a network of defects to live inside a domain wall in models of three real scalar fields, engendering the Z_2 x Z_3 symmetry. The field that governs the Z_2 symmetry generates a domain wall, and entraps the hexagonal…
Gapped domain walls, as topological line defects between 2+1D topologically ordered states, are examined. We provide simple criteria to determine the existence of gapped domain walls, which apply to both Abelian and non-Abelian topological…
We investigate domain wall junctions in a generalized Wess-Zumino model with a Z(N) symmetry. We present a method to identify the junctions which are potentially BPS saturated. We then use a numerical simulation to show that those junctions…
We investigate domain walls between 2d gapped phases of Turaev-Viro type topological quantum field theories (TQFTs) by constructing domain wall tube algebras. We begin by analyzing the domain wall tube algebra associated with bimodule…
We define a Turaev-Viro-Barrett-Westbury state sum model of triangulated 3-manifolds with surface, line and point defects. Surface defects are oriented embedded 2d PL submanifolds and are labeled with bimodule categories over spherical…
Levin-Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres. We generalise this construction to…
We investigate the presence of domain walls in models described by three real scalar fields. We search for stable defect structures which minimize the energy of the static field configurations. We work out explict orbits in field space and…
Domain wall networks on the surface of a soliton are studied in a simple theory. It consists of two complex scalar fields, in (3+1)-dimensions, with a global U(1) x Z_n symmetry, where n>2. Solutions are computed numerically in which one of…
The generalized quantum double lattice realization of 2d topological orders based on Hopf algebras is discussed in this work. Both left-module and right-module constructions are investigated. The ribbon operators and the classification of…
Elliptic boundary value problems which are posed on a random domain can be mapped to a fixed, nominal domain. The randomness is thus transferred to the diffusion matrix and the loading. While this domain mapping method is quite efficient…
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the {\it correct} cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the…
We review the key steps of the construction of Levin-Wen type of models on lattices with boundaries and defects of codimension 1,2,3 in a joint work with Alexei Kitaev. We emphasize some universal properties, such as boundary-bulk duality…
Levin-Wen models are microscopic spin models for topological phases of matter in (2+1)-dimension. We introduce a generalization of such models to (3+1)-dimension based on unitary braided fusion categories, also known as unitary premodular…
We address the problem of domain generalization where a decision function is learned from the data of several related domains, and the goal is to apply it on an unseen domain successfully. It is assumed that there is plenty of labeled data…
We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…