# Spin TQFTs and fermionic phases of matter

@inproceedings{Gaiotto2016SpinTA, title={Spin TQFTs and fermionic phases of matter}, author={Davide Gaiotto and Anton Kapustin}, year={2016} }

We study lattice constructions of gapped fermionic phases of matter. We show that the construction of fermionic Symmetry Protected Topological orders by Gu and Wen has a hidden dependence on a discrete spin structure on the Euclidean space-time. The spin structure is needed to resolve ambiguities which are otherwise present. An identical ambiguity is shown to arise in the fermionic analog of the string-net construction of 2D topological orders. We argue that the need for a spin structure is a… CONTINUE READING

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 43 CITATIONS

## On gapped boundaries for SPT phases beyond group cohomology

VIEW 9 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## Pin TQFT and Grassmann integral

VIEW 12 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## Spin topological field theory and fermionic matrix product states

VIEW 9 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Quantization of super Teichmüller spaces

VIEW 6 EXCERPTS

CITES RESULTS

HIGHLY INFLUENCED

## Fermionic SPT phases in higher dimensions and bosonization

VIEW 10 EXCERPTS

CITES RESULTS, BACKGROUND & METHODS

HIGHLY INFLUENCED

## Unoriented 3d TFTs

VIEW 4 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## B 98 , 125101 ( 2018 ) Spin topological field theory and fermionic matrix product states

VIEW 8 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Abelian Topological Order on Lattice with Electromagnetic Background

VIEW 10 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Fermi/Pauli Duality in Arbitrary Dimension

VIEW 6 EXCERPTS

CITES BACKGROUND & METHODS

HIGHLY INFLUENCED

## Bosonization in three spatial dimensions and a 2-form gauge theory

VIEW 3 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 26 REFERENCES

## Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Two-Dimensional State Sum Models and Spin Structures

VIEW 1 EXCERPT

## talk at the IPAM workshop “Symmetry and Topology in Quantum Matter,

## talk at the IPAM workshop “Symmetry and Topology in Quantum Matter,

VIEW 2 EXCERPTS

## Lattice model for fermionic toric code

VIEW 1 EXCERPT