# O ct 2 02 1 Interacting SPT phases are not Morita invariant

@inproceedings{Stehouwer2021OC2, title={O ct 2 02 1 Interacting SPT phases are not Morita invariant}, author={Luuk Stehouwer}, year={2021} }

Class D topological superconductors have been described as invertible topological phases protected by charge Q and particle-hole symmetry C. A competing description is that class D has no internal symmetries except for the fermion parity group ZF2 = {1, (−1) F }. In the weakly interacting setting, it can be argued that ‘particle-hole symmetry cancels charge’ in a suitable sense. Namely, the classification results are independent of which of the two internal symmetry groups are taken because of…

## One Citation

Rigorous Index Theory for One-Dimensional Interacting Topological Insulators

- Mathematics
- 2021

We present a rigorous but elementary index theory for a certain class of one-dimensional systems of interacting fermions that includes the Su-Schrieffer-Heeger (SSH) model as a special case. We prove…

## References

SHOWING 1-10 OF 27 REFERENCES

Periodic table for topological insulators and superconductors

- Physics, Mathematics
- 2009

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a…

Fermion Path Integrals And Topological Phases

- Physics
- 2016

Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here, we…

Symmetry Protected Topological phases of Quantum Matter

- Physics
- 2015

We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated…

Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures

- Physics
- 1997

Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron’s spin. Four symmetry classes are…

Classification of topological insulators and superconductors in three spatial dimensions

- Physics
- 2008

We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial…

Fermionic symmetry protected topological phases and cobordisms

- Physics
- 2014

A bstractIt has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with…

Twisted Equivariant Matter

- Mathematics, Physics
- 2012

We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical threefold way of real/complex/…

A new SU(2) anomaly

- PhysicsJournal of Mathematical Physics
- 2019

A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in…

Reflection positivity and invertible topological phases

- Mathematics, Physics
- 2016

We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable…

Pin Structures on Low-dimensional Manifolds by

- Mathematics
- 2008

Pin structures on vector bundles are the natural generalization of Spin structures to the case of non-oriented bundles. Spin(n) is the central Z/2Z extension (or double cover) of SO(n) and Pin-en)…