Physics behind the minimum of relative entropy measures for correlations

Abstract

The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal for the uncorrelated reference state that has the same one-particle density matrix as the correlated state. Hence, this particular measure, coined nonfreeness, is unique and reasonable. We demonstrate that for relevant physical situations, such as finite temperatures or a correlation enhanced orbital splitting, other choices of the uncorrelated state, even educated guesses, overestimate correlations.

4 pages, 1 figure, final version as to appear European Physical Journal B

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• Quantum criticality
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• Electronic entanglement in late transition metal oxides
• Von Neumann Entropy Spectra and Entangled Excitations in Spin-Orbital Models
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Cited by in corpus (5)

• Optimal multi-configuration approximation of an N-fermion wave function
• Entanglement Driven Phase Transitions in Spin-Orbital Models
• Correlation in fermion or boson systems as the minimum of entropy relative to all free states
• Nonfreeness and related functionals for measuring correlation in many-fermion states
• Mott metal-insulator transition in a modified periodic Anderson model: Insights from entanglement entropy and role of short-range spatial correlations