Fidelity susceptibility and geometric response in flux-tuned Dirac systems: exact results from a low-energy two-level reduction

Abstract

We study the parametric sensitivity of two-dimensional massive Dirac fermions subject to Aharonov-Bohm flux insertion, using the Bures metric (fidelity susceptibility) as the central statistical-mechanical response function. Near integer values of the reduced flux, the low-energy spectrum undergoes a flux-induced avoided crossing whose structure is controlled by the Dirac mass. Through a controlled low-energy projection of the full Dirac=Aharonov-Bohm operator onto an effective two-level subspace, valid near integer flux, we derive an exact closed-form expression for the ground-state Bures metric, which takes a universal Lorentzian profile centered at integer flux with width set by the mass parameter. The peak value scales as $g^{\max}_{λλ}\sim m^{-2}$, diverging in the chiral limit in direct analogy with the divergence of thermodynamic susceptibilities near critical points. We introduce an integrated geometric susceptibility $χ(m) = π/(8m)$, whose inverse-mass scaling is the information-geometric counterpart of power-law critical behavior, with the Dirac mass playing the role of a relevant coupling controlling the distance from the chiral fixed point. The Lorentzian profile is shown to arise from the curvature of the ground-state manifold on the Bloch sphere, requiring no dynamical input beyond the spectral structure. Importantly, this geometric response is independent of Berry curvature and topological invariants, emerging instead from a universal local spectral mechanism. Through its spectral representation, the Bures metric is identified as the geometric (paramagnetic) contribution to the persistent current susceptibility, encoding the sensitivity of persistent currents and orbital magnetization to flux variations and connecting information geometry to measurable response functions in mesoscopic Dirac systems.