相关论文: Categories of quantum liquids III

We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd's work on condensation completion. Based on this theory, we prove some fundamental results on $E_m$-multi-fusion higher categories and their…

We continue to develop the theory of separable higher categories, including center functors, higher centralizers, modular extensions and group theoretical higher fusion categories. Moreover, we outline a theory of orthogonal higher…

We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…

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…

In this paper, we introduce a generalized topological quantum field theory based on the symmetric monoidal category which we call causal network condensation since it can be regarded as a generalization of spin network construction of Baez,…

In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…

Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction,…

Conformal nets are a mathematical model for conformal field theory, and defects between conformal nets are a model for an interaction or phase transition between two conformal field theories. In the preceding paper of this series, we…

The existence of quantum non-liquid states and fracton orders, both gapped and gapless states, challenges our understanding of phases of entangled matter. We generalize the cellular topological states to liquid or non-liquid cellular…

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…

This is a comprehensive review on fault-tolerant topological quantum computation with the surface codes. The basic concepts and useful tools underlying fault-tolerant quantum computation, such as universal quantum computation, stabilizer…

We study generalized symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. This paper follows our companion paper on gapped phases and anomalies associated with these symmetries. In the present…

We consider the topological defect lines commuting with the spectral flow and the $\mathcal{N}=(4,4)$ superconformal symmetry in two dimensional non-linear sigma models on K3. By studying their fusion with boundary states, we derive a…

We propose a unifying mathematical framework describing the higher categorical structures formed by topological defects in quantum field theory equipped with tangential structures, such as orientations, framings, or…

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…

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…

We describe a coordinate-free notion of conformal nets as a mathematical model of conformal field theory. We define defects between conformal nets and introduce composition of defects, thereby providing a notion of morphism between…

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…

In the framework of the Closed-Time-Path formalism, we show how topological defects may arise in Quantum Field Theory as result of a localized (inhomogeneous) condensation of particles. We demonstrate our approach on two examples; kinks in…

In this paper, the key ideas of characterizing universality classes of dissipation-free (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many general theorems about the classification…