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Universality in phase diagrams separating QRSPTs and trivial phases

Ascertain whether universal patterns exist in the phase diagrams delineating quantum restored symmetry protected topological (QRSPT) phases from topologically trivial phases across models of fermions coupled to fluctuating order parameters.

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Background

The paper’s 1D model exhibits a QRSPT phase, a superconducting phase, and a trivial insulating phase, with critical behavior near the free-fermion transition modified by fluctuations. The authors identify edge phenomena and entanglement signatures supporting QRSPT order.

Whether such qualitative and quantitative structures in the phase diagram—such as the presence and nature of intervening critical lines or phases—display universal features beyond the specific model remains unresolved.

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