Natural orbitals in relation to quantum information theory: from model light atoms through to emergent metallic properties

Abstract

The review begins with a consideration of 3 forms of quantum information entropy associated with Shannon and Jaynes. For model two-electron spin compensated systems, some analytic progress is first reported. The Jaynes entropy is clearly related to correlation kinetic energy. A way of testing the usefulness of a known uncertainty principle inequality is proposed for a whole class of model two-electron atoms with harmonic confinement but variable electron-electron interaction. Emerging properties are then studied by reference to bcc Na at ambient pressure and its modeling by `jellium'. Jellium itself has collective behaviour with changes of the density, especially noteworthy being the discontinuity of the momentum distribution at the Fermi surface. This has almost reduced to zero at $r_s=100$ a.u., the neighbourhood in which the quantal Wigner electron solid transition is known to occur. However, various workers have studied crystalline Na under pressure and their results are compared and contrasted. Work by DFT on K, Rb, and Cs is discussed, but now with reduced density from the ambient pressure value. The crystalline results for the cohesive energy of these metals as a function of lattice parameters and local coordination number are shown to be closely reproduced by means of ground and excited states for dimer potential energy curves. Then, pair potentials for liquid Na and Be are reviewed, and compared with the results of computer simulations from the experimental structure factor for Na. Finally, magnetic field effects are discussed. First a phenomenological model of the metal-to-insulator transition is presented with an order parameter which is the discontinuity in the Fermi momentum distribution. Lastly, experiments on a two-dimensional electron assembly in a GaAs/AlGaAs heterojunction in a perpendicular magnetic field are briefly reviewed and then interpreted.

References in corpus (12)

• Transparent dense sodium
• Long-distance entanglement in spin systems
• Pinning of Fermionic Occupation Numbers
• Tetrahedral clustering in molten lithium under pressure
• Interstitial Electronic Localization
• Sodium: a charge-transfer insulator at high pressures
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Lindemann Criterion and the Anomalous Melting Curve of Sodium
• Plasmons in Sodium under Pressure: Increasing Departure from Nearly-Free-Electron Behavior
• Proposed definitions of the correlation energy density from a Hartree-Fock starting point: The two-electron Moshinsky model atom as an exactly solvable model
• Symmetry breaking and restoring under high pressure: the amazing behaviour of the "simple" alkali metals
• Statistical correlations of an anyon liquid at low temperatures

Cited by in corpus (4)

• Natural orbitals and two-particle correlators as tools for analysis of effective exchange couplings in solids
• Insights gained from solvable models into a variety of phase transitions, including emergent assemblies plus isoelectronic series of atomic ions
• Information and complexity measures in the interface of a metal and a superconductor
• Fingerprints of antiaromaticity in the negative ion (Li${}_3$Al${}_4$)${}^{-}$ via an ab initio quantum-chemical study of the equilibrium structure of the inhomogeneous electron liquid