# 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} }

## 98 Citations

### Topological quantum field theory for Abelian topological phases and loop braiding statistics in (3+1) -dimensions

- PhysicsPhysical Review B
- 2019

Topological quantum field theory (TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In 2+1d, it is well known that the Chern-Simons theory captures all the…

### Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions

- Physics
- 2018

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…

### Topological orders, braiding statistics, and mixture of two types of twisted BF theories in five dimensions

- PhysicsJournal of High Energy Physics
- 2022

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…

### Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

- Physics
- 2017

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…

### Non-Abelian three-loop braiding statistics for 3D fermionic topological phases

- PhysicsNature Communications
- 2021

Fractional statistics is one of the most intriguing features of topological phases in 2D. In particular, the so-called non-Abelian statistics plays a crucial role towards realizing topological…

### Quantum statistics and spacetime topology: Quantum surgery formulas

- PhysicsAnnals of Physics
- 2019

### Non-Abelian gauged fracton matter field theory: Sigma models, superfluids, and vortices

- PhysicsPhysical Review Research
- 2020

By gauging a higher-moment polynomial degree global symmetry and a discrete charge conjugation (i.e., particle-hole) symmetry coupled to matter fields (two symmetries mutually non-commutative), we…

### Bosonic topological phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging

- PhysicsPhysical Review B
- 2018

We analyze $2+1d$ and $3+1d$ Bosonic Symmetry Protected Topological (SPT) phases of matter protected by onsite symmetry group $G$ by using dual bulk and boundary approaches. In the bulk we study an…

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

- MathematicsPhysical Review X
- 2019

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,…

### Quantum 4d Yang-Mills theory and time-reversal symmetric 5d higher-gauge topological field theory

- PhysicsPhysical Review D
- 2019

We explore various 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short-/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal…

## References

SHOWING 1-10 OF 104 REFERENCES

### Topological invariants for gauge theories and symmetry-protected topological phases

- Mathematics
- 2015

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

- Mathematics
- 2017

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

- Physics
- 2016

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

- Mathematics
- 2015

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.

- PhysicsPhysical review letters
- 2015

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.

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

- Physics, Mathematics
- 2017

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

- Mathematics
- 2014

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

- Physics
- 2014

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

- Physics
- 2005

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,''…