Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions

@article{Putrov2016BraidingSA,
  title={Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions},
  author={Pavel Putrov and Juven C. Wang and Shing-Tung Yau},
  journal={arXiv: Strongly Correlated Electrons},
  year={2016}
}
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References

SHOWING 1-10 OF 104 REFERENCES

Topological invariants for gauge theories and symmetry-protected topological phases

We study the braiding statistics of particlelike and looplike excitations in two- (2D) and three-dimensional (3D) gauge theories with finite, Abelian gauge group. The gauge theories that we consider…

Wilson operator algebras and ground states of coupled BF theories

The multi-flavor $BF$ theories in (3+1) dimensions with cubic or quartic coupling are the simplest topological quantum field theories that can describe fractional braiding statistics between…

Topological quantum field theory of three-dimensional bosonic Abelian-symmetry-protected topological phases

Symmetry-protected topological phases (SPT) are short-range entangled gapped states protected by global symmetry. Nontrivial SPT phases cannot be adiabatically connected to the trivial disordered…

Non-Abelian string and particle braiding in topological order: Modular SL ( 3 , Z ) representation and ( 3 + 1 ) -dimensional twisted gauge theory

String and particle braiding statistics are examined in a class of topological orders described by discrete gauge theories with a gauge group G and a 4-cocycle twist ω 4 of G 's cohomology group H 4…

Field-theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology, and beyond.

Gauge fields are used to represent those symmetry twists in closed spacetimes of any dimensionality and arbitrary topology and show that SPT invariants of pure gauge actions describe the SPTs predicted by group cohomology, while the mixed gauge-gravityactions describe the beyond-group-cohomology SPTs.

Quantum field theory of non-abelian strings and vortices

Towards a Complete Classification of Symmetry-Protected Topological Phases for Interacting Fermions in Three Dimensions and a General Group Supercohomology Theory

Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been…

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…

Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory

Symmetry-protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry $G$, which can all be smoothly connected to the trivial product states if we break the…

String-net condensation: A physical mechanism for topological phases

We show that quantum systems of extended objects naturally give rise to a large class of exotic phases---namely topological phases. These phases occur when extended objects, called ``string-nets,''…
...