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Classification of QRSPT phases given an underlying free-fermion SPT and mean-field SSB

Determine which quantum restored symmetry protected topological (QRSPT) phases can occur for a specified underlying free-fermion symmetry protected topological phase together with a given mean-field spontaneous symmetry breaking pattern of the protecting symmetry.

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Background

QRSPTs arise when a symmetry that protects a free-fermion SPT is broken at the mean-field level but restored on long timescales by quantum fluctuations, leading to topological features distinct from the original free system. The authors’ concrete model displays a QRSPT phase stabilized by the interplay of fermions and fluctuating superconducting order.

A general classification principle that predicts which QRSPT phases emerge from a chosen free-fermion SPT and a prescribed pattern of mean-field symmetry breaking is not known; establishing such a mapping would systematize the constructive design of QRSPTs.

References

While it is generally expected that insulating QRSPTs are related to topological zeros in the fermionic Green's function , we leave this as an open question for future studies along with, first, which QRSPT phases can be expected based on a given underlying free fermion SPT and mean-field SSB, second, whether there are universal patterns in the corresponding phase diagram between QRSPT and trivial phase, and third, a careful analysis in higher dimensions.

— Quantum Restored Symmetry Protected Topological Phases (2410.02689 - Tiwari et al., 3 Oct 2024) in Conclusion