Classification of 3+1D Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions

@article{Lan2019ClassificationO,
  title={Classification of 
3+1D
 Bosonic Topological Orders (II): The Case When Some Pointlike Excitations Are Fermions},
  author={Tian Lan and Xiao-Gang Wen},
  journal={Physical Review X},
  year={2019}
}
  • T. Lan, X. Wen
  • Published 25 January 2018
  • Mathematics
  • Physical Review X
We call a topological order of 3+1-dimensional bosonic systems an all-boson (AB) topological order if all emergent point-like excitations are bosons. It was shown that AB topological orders, $\mathcal C^4_{AB}$, are classified by unitary pointed fusion 2-categories with only trivial 1-morphisms. In fact, AB topological orders can all be realized by Dijkgraaf-Witten gauge theories. In this paper, we consider emergent-fermion (EF) topological orders for 3+1D bosonic systems where some emergent… 
(3+1)D topological orders with only a $\mathbb{Z}_2$-charged particle
There is exactly one bosonic (3+1)-dimensional topological order whose only nontrivial particle is an emergent boson: pure $\mathbb{Z}_2$ gauge theory. There are exactly two (3+1)-dimensional
Topological Orders, Braiding Statistics, and Mixture of Two Types of Twisted $BF$ Theories in Five Dimensions
Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological
Lattice models that realize Zn -1 symmetry-protected topological states for even n
Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high-energy scales while other topological excitations have
Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which describe the dynamics
Topological quantum field theory, symmetry breaking, and finite gauge theory in 3+1D
We derive a canonical form for 2-group gauge theory in 3+1D which shows they are either equivalent to Dijkgraaf-Witten theory or to the so-called "EF1" topological order of Lan-Wen. According to that
Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3+1D topological orders for boson systems
A discrete nonlinear $\ensuremath{\sigma}$-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 simplicial
Topological Orders in (4+1)-Dimensions
We investigate the Morita equivalences of (4+1)-dimensional topological orders. We show that any (4+1)-dimensional super (fermionic) topological order admits a gapped boundary condition — in other
Construction and Classification of Symmetry-Protected Topological Phases in Interacting Fermion Systems
The classification and lattice model construction of symmetry protected topological (SPT) phases in interacting fermion systems are very interesting but challenging. In this paper, we give a
Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a
Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
We formulate a family of spin Topological Quantum Field Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf–Witten TQFTs. They are obtained by gauging G -equivariant invertible
...
...

References

SHOWING 1-10 OF 70 REFERENCES
Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons
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
Theory of (2+1)-dimensional fermionic topological orders and fermionic/bosonic topological orders with symmetries
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
Classification of (2+1)-dimensional topological order and symmetry-protected topological order for bosonic and fermionic systems with on-site symmetries
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,
Exactly soluble local bosonic cocycle models, statistical transmutation, and simplest time-reversal symmetric topological orders in 3+1 dimensions
We propose a generic construction of exactly soluble \emph{local bosonic models} that realize various topological orders with gappable boundaries. In particular, we construct an exactly soluble
Universal topological data for gapped quantum liquids in three dimensions and fusion algebra for non-Abelian string excitations
Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the
Three-dimensional topological lattice models with surface anyons
We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they
Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
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
Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
We study Abelian braiding statistics of loop excitations in three-dimensional (3D) gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic
Generalized Modular Transformations in (3+1)D Topologically Ordered Phases and Triple Linking Invariant of Loop Braiding
In topologically ordered quantum states of matter in 2+1D (space-time dimensions), the braiding statistics of anyonic quasiparticle excitations is a fundamental characterizing property which is
...
...