Correlation Paradox of the Dissociation Limit: A Quantum Information Perspective

The interplay between electron interaction and geometry in a molecular system can lead to rather paradoxical situations. The prime example is the dissociation limit of the hydrogen molecule. While a significant increase of the distance r between the two nuclei marginalizes the electron-electron interaction, the exact ground state does, however, not take the form of a single Slater determinant. By first reviewing and then employing concepts from quantum information theory, we resolve this paradox and its generalizations to more complex systems in a quantitative way. To be more specific, we illustrate and prove that thermal noise due to finite, possibly even just infinitesimally low, temperature T will destroy the entanglement beyond a critical separation distance r_crit(T) entirely. Our analysis is comprehensive in the sense that we simultaneously discuss both total correlation and entanglement in the particle picture as well as in the orbital/mode picture. Our results reveal a conceptually new characterization of static and dynamical correlation in ground states by relating them to the (non)robustness of correlation with respect to thermal noise.