Many-body Hamiltonians Heisenberg model

To reasonably limit the focus here it the survey is primarily of many-body solution techniques as applied to a particular VB model, the covalent-space Pauling-Wheland VB model, represented by the Heisenberg spin Hamiltonian... 

This highly unorthodox model of the conducting solid cannot explain the conductivity, although it is not incompatible with it since the wave operator fl would build ionic components from the projected (neutral-only) wavefunc-tion. From the principles, and as shown by the previously mentioned success of Heisenberg Hamiltonians on the most metallic chemical systems (aromatic molecules), almost any system of which the lowest VB determinants are neutral may be treated either by the independent-particle approach followed by a treatment of electronic correlation which reduces the ionic compo-nents or by a Heisenberg-type effective Hamiltonian. This statement seems to be true whatever the p/U ratio. Malrieu et also noticed that the many-body effects (for instance four-body cyclic contributions), which are so important on small molecules and clusters, play a much less important role in the solid. 

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