# Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions

## TL;DR

This paper explores how density functional theory and information-theoretic tools can detect quantum phase transitions with high precision.

## Contribution

It introduces a novel framework linking DFT with information measures like fidelity and Rényi entropy to diagnose quantum criticality.

## Key findings

- Fidelity shows pronounced curvature near the critical point in the Dicke model.
- Information-theoretic measures are proportional in the small-parameter-shift regime.
- The response of these measures sharpens with increasing system size.

## Abstract

Within density functional theory (DFT), where the density is the fundamental variable, quantum phase transitions (QPTs) can be formulated through a Hamiltonian H^=H^0+∑iξiA^i, such that the control parameters {ξi} are in bijective correspondence (in the nondegenerate case) with the “densities” ai=〈A^i〉, 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.