Determine the ultraviolet-dependent insulating thresholds and SWSSB plateaus

Determine the ultraviolet-dependent insulating thresholds for strong-to-weak spontaneous symmetry breaking and the values of the SWSSB correlation plateaus by directly analyzing the compact XY models associated with the Renyi correlators.

Background

The paper maps Renyi correlators of infinitely dephased fermionic states to compact XY models. For insulating parent states, the existence of an SWSSB phase depends on the renormalized stiffness, which is controlled by ultraviolet details and cannot be fixed solely by the infrared power-counting analysis. The long-distance theory therefore predicts possible ordered and disordered phases but not their quantitative phase boundaries.

The authors also identify the plateau values of the long-range SWSSB correlators as nonuniversal quantities. Because the perturbative methods used in the paper have no small parameter at the lattice scale, both the insulating thresholds and plateau values require a direct, nonperturbative study of the corresponding XY models.

References

Several questions remain open. The perturbative methods have no small parameter at the lattice scale, so the location of the insulating thresholds, and the value of the SWSSB plateaus, are UV dependent quantitative questions that call for a direct study of the XY model of Sec.~\ref{sec:xy}.

— Strong-to-Weak Spontaneous Symmetry Breaking of Dephased Fermions  (2609.37965 - Sarma, 29 Sep 2026) in Section Conclusions

That $\rho_s$ remains finite at $t=\infty$ is the mean-field prediction, confirmed by numerics and experiment in $d=2$, but it is not established by a controlled calculation.

— Strong-to-Weak Spontaneous Symmetry Breaking of Dephased Fermions  (2609.37965 - Sarma, 29 Sep 2026) in Section 7.2, Replica field theory from the doubled state representation

For this choice of the density matrix it has been conjectured that SWSSB is ubiquitous in the thermodynamic limit :

— Emergent Symmetries in Ensemble Averages  (2609.36542 - Yamazaki, 29 Sep 2026) in Section 6.4, “How General is SWSSB?”