相关论文: Anyon condensation and tensor categories
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
A finite bosonic or fermionic symmetry can be described uniquely by a symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are classified, up to $E_8$…
Given a braided tensor *-category C with conjugate (dual) objects and irreducible unit together with a full symmetric subcategory S we define a crossed product C\rtimes S. This construction yields a tensor *-category with conjugates and an…
For a braided tensor category C and a subcategory K there is a notion of centralizer C_C(K), which is a full tensor subcategory of C. A pre-modular tensor category is known to be modular in the sense of Turaev iff the center Z_2(C):=C_C(C)…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
Anyons with a statistical phase parameter $\alpha\in(0,2)$ are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduction for a 2D system of anyons in a tight wave-guide.…
We propose a framework for producing interesting subcategories of the category ${}_A\mathsf{Mod}$ of left $A$-modules, where $A$ is an associative algebra over a field $k$. The construction is based on the composition, $Y$, of the Yoneda…
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its…
The c=1 matrix model, with or without a type 0 hat, has an exact quantum solution corresponding to closed string tachyon condensation along a null surface. The condensation occurs, and spacetime dissolves, at a finite retarded time on I^+.…
In this note, we introduce monoidal subcategories of the tensor category of finite-dimensional representations of a simply-laced quantum affine algebra, parametrized by arbitrary Dynkin quivers. For linearly oriented quivers of types A and…
A C*-tensor category with simple unit object is realized by von Neumann algebra bimodules of finite Jones index if and only if it is rigid.
Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion…
We introduce a modified 2D toric code Hamiltonian that exhibits explicit anyon confinement along a single spatial direction. By bounding the motion of these confined anyons, we obtain dipolar excitations with restricted mobility. We analyze…
In this paper a new theory is developed for the self - assembly of associating molecules confined to a single spatial dimension, but allowed to explore all orientation angles. The interplay of the anisotropy of the pair potential and the…
Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the…
Topological phases exhibit unconventional order that cannot be detected by any local order parameter. In the framework of Projected Entangled Pair States(PEPS), topological order is characterized by an entanglement symmetry of the local…
We develope $\mathbb{C}^{\ast}$-equivariant categorical Donaldson-Thomas theory for local surfaces, i.e. the total spaces of canonical line bundles on smooth projective surfaces. We introduce $\mathbb{C}^{\ast}$-equivariant DT categories…
We derive new dualities of topological quantum field theories in three spacetime dimensions that generalize the familiar level-rank dualities of Chern-Simons gauge theories. The key ingredient in these dualities is non-abelian anyon…
A complex $C^\bullet(C,D)(F,G)(\eta, \theta)$, generalising the Davydov-Yetter complex of a monoidal category, is constructed. Here $C,D$ are $\Bbbk$-linear (dg) monoidal categories, $F,G\colon C\to D$ are $\Bbbk$-linear (dg) strict…
We study symmetries and defects of a wide class of two dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles…