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Density Functional Theory and Information-Theoretic Diagnostics of Quantum Phase Transitions
1Departamento de Física Atómica, Molecular y Nuclear and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain.
Entropy (Basel, Switzerland)
|February 27, 2026
Summary
Density functional theory (DFT) enables quantum phase transitions (QPTs) formulation using information-theoretic measures like fidelity. These measures precisely diagnose criticality in models like the Dicke model, showing enhanced sensitivity with system size.
Area of Science:
- Quantum physics
- Computational chemistry
- Information theory
Background:
- Density Functional Theory (DFT) is a quantum mechanical modeling method that uses the electron density as the basic quantum mechanical observable.
- Quantum Phase Transitions (QPTs) are changes in the ground state properties of quantum systems at absolute zero temperature.
- Information-theoretic measures offer novel ways to probe quantum phenomena.
Purpose of the Study:
- To formulate Quantum Phase Transitions (QPTs) within Density Functional Theory (DFT).
- To investigate the utility of information-theoretic measures as sensitive diagnostics for QPTs.
- To apply these methods to the Dicke model and analyze their performance.
Main Methods:
- Formulation of QPTs in DFT using a Hamiltonian with control parameters linked to densities.
- Application of information-theoretic measures: fidelity, Fisher information, Rényi entropy, and Kullback-Leibler divergence.
- Numerical analysis of the Dicke model to evaluate the behavior of these measures near criticality.
Main Results:
- Information-theoretic measures are shown to be proportional in the small-parameter-shift regime (Rq≈qIKL≈2qχ(δλ)2).
- Fidelity exhibits significant curvature or divergence at the critical point (λc=ωω0/2) in the Dicke model.
- The sensitivity of these measures to QPTs increases with system size (j).
Conclusions:
- Information-theoretic measures provide a precise and sensitive framework for diagnosing QPTs within DFT.
- The established link between information measures and QPTs is robust and applicable to complex quantum models.
- This approach offers a powerful tool for understanding quantum criticality in various physical systems.
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