Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions Romera Gutiérrez, Elvira Nagy, Agnes Density functional theory Quantum phase transitions Rényi entropy Within density functional theory (DFT), where the density is the fundamental vari able, quantum phase transitions (QPTs) can be formulated through a Hamiltonian H = ˆH0+∑iξi ˆAi, such that the control parameters {ξi} are in bijective correspondence (in the nondegenerate case) with the “densities” ai = ⟨ ˆAi⟩, 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≈ q IKL≈ 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. 2026-02-02T11:34:37Z 2026-02-02T11:34:37Z 2026-02-01 journal article Romera, E., & Nagy, Á. (2026). Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions. Entropy, 28(2), 170. https://doi.org/10.3390/e28020170 https://hdl.handle.net/10481/110582 10.3390/e28020170 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional MDPI