Related papers: A classification of 2D fermionic and bosonic topol…
In this paper, we classify EF topological orders for 3+1D bosonic systems where some emergent pointlike excitations are fermions. (1) We argue that all 3+1D bosonic topological orders have gappable boundary. (2) All the pointlike…
$2+1$D bosonic topological orders can be characterized by the $S,T$ matrices that encode the statistics of topological excitations. In particular, the $S,T$ matrices can be used to systematically obtain the gapped boundaries of bosonic…
We propose that, up to invertible topological orders, 2+1D fermionic topological orders without symmetry and 2+1D fermionic/bosonic topological orders with symmetry $G$ are classified by non-degenerate unitary braided fusion categories…
Gapped quantum liquids (GQL) include both topologically ordered states (with long range entanglement) and symmetry protected topological (SPT) states (with short range entanglement). In this paper, we propose a classification of 2+1D GQL…
We use a 2-categorical version of (de-)equivariantization to classify (3+1)d topological orders with a finite $G$-symmetry. In particular, we argue that (3+1)d fermionic topological order with $G$-symmetry correspond to…
Gravitational anomalies can be realized on the boundary of topologically ordered states in one higher dimension and are described by topological orders in one higher dimension. In this paper, we try to develop a general theory for both…
In this work we consider general fermion systems in two spatial dimensions, both with and without charge conservation symmetry, which realize a nontrivial fermionic topological order with only Abelian anyons. We address the question of…
The 2+1D topological order can be characterized by the mapping-class-group representations for Riemann surfaces of genus-1, genus-2, etc. In this paper, we use those representations to determine the possible gapped boundaries of a 2+1D…
Topological orders are a class of phases of matter that beyond the Landau symmetry breaking paradigm. The two (spatial) dimensional (2d) topological orders have been thoroughly studied. It is known that they can be fully classified by a…
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…
Topological orders are new phases of matter beyond Landau symmetry breaking. They correspond to patterns of long-range entanglement. In recent years, it was shown that in 1+1D bosonic systems there is no nontrivial topological order, while…
The Z_2 topological order in Z_2 spin liquid and in exactly soluble Kitaev toric code model is the simplest topological order for 2+1D bosonic systems. More general 2+1D bosonic topologically ordered states can be constructed via exact…
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 provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$ and general values of the chiral central charge $c_-$. Here $G_f$ is a…
The unified mathematical theory of gapped and gapless edges of 2d topological orders was developed by two of the authors. It provides a powerful tool to study pure edge topological phase transitions on the edges of 2d topological orders…
Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry protected topological orders exist. In this paper, we…
This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological…
We discuss the codimension-1 defects of (2+1)D bosonic topological phases, where the defects can support fermionic degrees of freedom. We refer to such defects as fermionic defects, and introduce a certain subclass of invertible fermionic…
We develop a systematic framework for understanding symmetries in topological phases in 2+1 dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon species and global symmetries permuting anyon species,…
The topological classifications of quadratic bosonic systems according to the symmetries of the dynamic matrices from the equations of motion of closed systems and the effective Hamiltonians from the Lindblad equations of open systems are…