Within density functional theory (DFT), where the density is the fundamental variable, quantum phase transitions (QPTs) can be formulated through a Hamiltonian H^=H⁰+∑iξiAⁱ, such that the control parameters ξi are in bijective correspondence (in the nondegenerate case) with the “densities” ai=⟨Aⁱ⟩, and the functional Q (ai) acts as the Legendre transform of the energy; this structure even permits the use of Rényi entropy (for a given order) as an alternative control parameter, while degeneracy can be handled via a subspace density. On this foundation, information-theoretic measures provide sensitive diagnostics of criticality: fidelity and its susceptibility χ, Fisher information, relative Rényi entropy, and the Kullback–Leibler divergence are locally linked by Rq≈qIKL≈2qχ (δλ) 2, revealing their proportionality in the small-parameter-shift regime. Applied to the Dicke model, numerical analyses show that fidelity exhibits pronounced curvature or divergence near λc=ωω0/2 and that the response sharpens with increasing j, corroborating that these information measures capture QPTs with precision within the DFT framework.
Romera et al. (2026) studied this question.