Spin TQFTs and fermionic phases of matter

By D. Gaiotto, A. Kapustin. 2015

191 citations recorded by the source corpus.

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 general feature of lattice models with local fermionic degrees of freedom and is a lattice analog of the spin-statistics relation.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/f6f351beba11ab1e93230d789bf5270f6b521b7e

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Reflection positivity and invertible topological phases (2016, methodology): “the homotopy groups of spheres \knows about" the bosonic/fermionic grading of quantum states. The next Z{2Z in the stable stem also has an interpretation in terms of statistics of particles; see [GK] where objects with nontrivial Z{2Z-grading are termed ‘Majorana’. 34 D. S. FREED AND M. J. HOPK”
State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter (2016, methodology): “For example, it has been proposed in [4] that 3+1d fermionic phases are related to bosonic phases with an anomalous 2-form Z2 symmetry, where the 5d anomaly action is ∫”
Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions (2016, background): “spin TQFTs) when p II is an odd integer. A fermionic TQFTs can emerge only from a fermionic Hamiltonian that contains fundamental fermionic operators satisfying the anti-commuting relations (see e.g. [41,42]). We emphasize that the fermionic quantum matter have fundamental fermions (also can have fu”
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases (2021, methodology): “[112, 113] it was stressed that the 1-form symmetry in 2+1D bosonization has an anomaly Sq 2 B (unlike in 1+1D bosonization where we obtain an anomaly-free Z 2 symmetry upon bosonizing) and the kernel of the bosonization transformation gives a trivializa-tion of this anomaly in the presence of…”