Rigorous treatment of symmetry-fixed charge sectors

Establish a rigorous treatment of symmetry-fixed charge sectors and their coupling to fluctuations of other Bethe-root densities when the initial state has an exactly fixed conserved charge, rather than incorporating the fixed direction through an independent delta-functional constraint.

Background

The BMFT–Quench Action construction assumes that the conserved charges retained as fluctuating hydrodynamic fields have a nontrivial extensive initial full-counting statistics. Some integrable initial states, including dimer states, can instead be exact eigenstates of magnetisation, particle number, or other charges, making the joint fluctuation measure singular and restricting it to a lower-dimensional manifold of root-density profiles.

In multicomponent Bethe-ansatz systems, fixing one charge may couple different string or species densities and alter the fluctuations of the remaining charges. The paper therefore does not assume that fixed directions can be appended as independent constraints and explicitly leaves their systematic treatment unresolved.

References

An exactly fixed charge does not necessarily destroy the large-deviation principle, but makes the joint fluctuation measure singular and restricts it to a lower-dimensional manifold of root-density profiles. In a multi-species Bethe-ansatz system this restriction can couple different string densities and may modify the fluctuations of the remaining charges. We therefore do not assume that every fixed direction can be incorporated by appending an independent delta-functional constraint to an otherwise unchanged measure. As argued in Appendix~\ref{app:overlap}, such non-extensive directions are nevertheless expected to be exceptional for finite-range parity-even charges in dimer-type integrable initial states. We apply QQ_BMFT_Init_Measure only in directions with a nontrivial extensive initial FCS; symmetry-fixed sectors and their coupling to other Bethe-root fluctuations are left for future work.

— Large-scale dynamics of integrable quenches  (2609.09139 - Horvath et al., 8 Sep 2026) in Section 3.1, subsection “The initial measure”