Microscopic Determination of Relaxed Domain-Wall Tensions

Determine the fully relaxed microscopic free energies of the lowest-energy chirality-changing and same-chirality translation domain walls in a material-specific kagome loop-current theory, and compare their ratio with the approximately 1.12–1.13 criterion for vestigial chiral order.

Background

The phenomenological sign and soft-spin models show that a vestigial chiral phase can occur when the chirality-changing domain wall is only about 12–13% more costly than the lowest-energy same-chirality translation wall in the rigid-amplitude limit. Amplitude relaxation modifies the threshold, so the relevant quantities are the fully relaxed wall free energies rather than the bare coupling ratio. The paper does not calculate these quantities for a specific kagome compound or microscopic electronic model, leaving this as the remaining material-specific problem.

References

Establishing the required counting bound, and determining whether wall proliferation produces a finite-temperature transition, are left for future work.

— Exact selection of a toric-code vison crystal in a flux-conditioned Kitaev model  (2609.29004 - Wang et al., 24 Sep 2026) in Section 5.4, subsection “Domain walls and incommensurate tori”

The remaining material question is therefore concrete: determine the two relaxed wall tensions microscopically or experimentally and compare their ratio with the criterion established here.

— Vestigial chirality from fluctuating loop currents on the kagome lattice  (2609.19618 - Shi et al., 17 Sep 2026) in Discussion, Section 'Relation to vestigial superconductivity and outlook'