Related papers: Fusing Binary Interface Defects in Topological Pha…
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…
A domain wall structure consists of a planar graph with faces labeled by fusion categories/topological phases. Edges are labeled by bimodules/domain walls. When the vertices are labeled by point defects we get a compound defect. We present…
Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is…
Integrable defects in two-dimensional integrable models are purely transmitting thus topological. By fusing them to integrable boundaries new integrable boundary conditions can be generated, and, from the comparison of the two solved…
Conformal nets provides a mathematical model for conformal field theory. We define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. We introduce an operation of fusion…
We consider two conformal defects close to each other in a free theory, and study what happens as the distance between them goes to zero. This limit is the same as zooming out, and the two defects have fused to another defect. As we zoom in…
We study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions stay invariant. This is an expected result as the path integral stays invariant under fusion of the two…
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 propose an experimentally feasible scheme for topological interface engineering and show how it can be used for studies of dynamics of topologically nontrivial interfaces and perforation of defects and textures across such interfaces.…
We define a class of lattice models for two-dimensional topological phases with boundary such that both the bulk and the boundary excitations are gapped. The bulk part is constructed using a unitary tensor category $\calC$ as in the…
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…
Using extensive Monte Carlo simulations, we test the hypothesis that the density of corresponding topological defects has an universal value at the temperature of a continuous phase transition. We consider several simple two-dimensional…
We revisit the problem of boundary excitations at a topological boundary or junction defects between topological boundaries in non-chiral bosonic topological orders in 2+1 dimensions. Based on physical considerations, we derive a formula…
The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive…
Topological defects are interfaces joining two conformal field theories, for which the energy momentum tensor is continuous across the interface. A class of the topological defects is provided by the interfaces separating two bulk systems…
In this paper, we propose a new type of bulk-boundary correspondence as a generic approach to theoretically and experimentally detect fragile topological states. When the fragile phase can be written as a difference of a trivial atomic…
We consider two $d \geq 2$ conformal field theories (CFTs) glued together along a codimension one conformal interface. The conformal anomaly of such a system contains both bulk and interface contributions. In a curved-space setup, we…
The binary Defect Combination Problem consists in finding a fully working subset from a given ensemble of imperfect binary components. We determine the typical properties of the model using methods of statistical mechanics, in particular,…
Finite depth quantum circuits provide an equivalence relation between gapped phases. Moreover, there can be nontrivial domain walls either within the same gapped phase or between different gapped phases, whose equivalence relations are…
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…