Higher-dimensional analysis of QRSPTs

Develop a careful analysis of quantum restored symmetry protected topological (QRSPT) phases in dimensions higher than one, including bulk and boundary properties and the role of long-wavelength fluctuations of order parameters that restore protecting symmetries.

Background

The QRSPT mechanism—failure of mean-field symmetry breaking due to strong quantum fluctuations restoring a protecting symmetry—should in principle operate beyond one dimension, potentially with distinct critical phenomena and topology in both bulk and edges or surfaces.

The present paper focuses on a one-dimensional system; extending the framework to higher dimensions would test the generality of QRSPTs and identify new topological features unique to higher-dimensional settings.

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., 2024) in Conclusion

At the moment, for fermion topological states we are not aware of a systematic way to derive these emergent symmetries from the protecting symmetry group $G_p$ and topological data such as boundary states.

— Holographic Representations of Topological Quantum Criticality: Emergent Symmetry Approach around the Bott Clock  (2608.30335 - Yang et al., 31 Aug 2026) in Section 1, Introduction