Finite-subsystem QFI edge topology

Determine, by evaluating the exact quantum Fisher information expression for the particle number in a finite subextensive subsystem of the quenched two-dimensional p+ip superfluid, whether the sign of the QFI spectrum immediately inside the phase-II continuum edges carries topological information when the large-subsystem condition is not satisfied.

Background

The paper derives the phase-II QFI spectrum primarily within the large-subsystem approximation, $L_A\gg k_s^{-1}$, where the two momenta entering the exact QFI expression can be treated as approximately equal. In that regime, when $\mu_\infty<m\Delta_\infty^2$, the QFI spectrum vanishes at the continuum edges and its sign immediately inside the edges directly reveals the pre-quench pseudospin winding number $Q$.

For finite subsystems with $L_A\lesssim k_s^{-1}$, the exact QFI involves pairs of distinct momenta. Although the spectrum still vanishes at the relevant edges, its sign depends on the pseudospin texture over a finite momentum window rather than solely on the zero-momentum pseudospin. The paper therefore leaves unresolved whether this finite-subsystem edge behavior retains any reliable information about the topology of the pre-quench state.