Related papers: Composing topological domain walls and anyon mobil…
A discrete non-linear $\sigma$-model is obtained by triangulate both the space-time $M^{d+1}$ and the target space $K$. If the path integral is given by the sum of all the complex homomorphisms $\phi: M^{d+1} \to K$, with an partition…
We study gauging operations (or group extensions) in (smeared) boundary conformal field theories (BCFTs) and bulk conformal field theories, and their applications to various phenomena in topologically ordered systems. We apply the resultant…
In this paper, we explore topological quantum computation augmented by subphases and phase transitions. We commence by investigating the anyon tunneling map, denoted as $\varphi$, between subphases of the quantum double model…
We propose a correspondence between topological order in 2+1d and Seifert three-manifolds together with a choice of ADE gauge group $G$. Topological order in 2+1d is known to be characterized in terms of modular tensor categories (MTCs),…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…
In this paper we will present some ideas to use 3D topology for quantum computing extending ideas from a previous paper. Topological quantum computing used \textquotedblleft knotted\textquotedblright{} quantum states of topological phases…
A scheme is proposed to construct integer and fractional topological quantum states of fermions in two spatial dimensions. We devise models for such states by coupling wires of non-chiral Luttinger liquids of electrons, that are arranged in…
Recent developments in unifying treatment of domain wall configurations and their global space-time structure is presented. Domain walls between vacua of non-equal cosmological constant fall in three classes depending on the value of their…
The natural existence of crystalline symmetry in real materials manifests the importance of understanding crystalline symmetry-protected topological (SPT) phases, especially for interacting systems. In this paper, we systematically…
We study anomalies in time-reversal ($\mathbb{Z}_2^T$) and $U(1)$ symmetric topological orders. In this context, an anomalous topological order is one that cannot be realized in a strictly $(2+1)$-D system but can be realized on the surface…
Domain walls in correlated charge density wave compounds such as 1T-TaS2 can have distinct localized states which govern physical properties and functionalities of emerging quantum phases. However, detailed atomic and electronic structures…
Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable…
In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…
We present old and new characterizations of core spaces, alias worldwide web spaces, originally defined by the existence of supercompact neighborhood bases. The patch spaces of core spaces, obtained by joining the original topology with a…
The hallmark of a 2 dimensional topologically ordered phase is the existence of deconfined `anyon' excitations that have exotic braiding and exchange statistics, different from those of ordinary bosons or fermions. As opposed to…
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…
A family of locally equivalent models is considered. They can be taken as a generalization to $d+1$ dimensions of the Topological Massive and ``Self-dual'' models in 2+1 dimensions. The corresponding 3+1 models are analized in detail. It is…
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry…
The fusion rules and braiding statistics of anyons in $(2+1)$D fermionic topological orders are characterized by the modular data of a super-modular category. On the other hand, the modular data of a super-modular category form a congruence…
Using a link between graph theory and the geometry hosting higher order topological matter, we fill part of the missing results in the engineering of domain walls supporting gapless states for systems with three vertical hinges. The…