Friday, April 1, 2011

Some key concepts in many-body physics

The two-site Hubbard model lives on!
This week I read two interesting papers 

Singlet Diradical Character from Experiment (a 2010 J. Phys. Chem. Lett.)

One thing that is fascinating about both papers is that essentially they are based on a two-site extended Hubbard model!

Indeed I think that studying and understanding the two-site Hubbard model is the first step in learning some of the key concepts associated with quantum many-body physics in both chemistry and solid state physics. It can be used to illustrate:
  • origin of covalent chemical bonding
  • splitting of singlet & triplet excited states
  • different energy scales for charge and spin excitations.
  •  tendency to charge localisation (Mott insulator)
  •  formation of local magnetic moments
  •  antiferromagnetic exchange spin interactions
  •  relation between valence bond and molecular orbital methods
  •  Configuration Interaction (CI)
  • symmetry is useful for labeling many-body states and diagonalising Hamiltonians
  • for widely separated (and/or spatially localised) atomic orbitals, electron-electron interactions become increasingly important.
  • Electronic correlation effects (entanglement), neglected by Hartree-Fock, can lead to significant qualitative differences.
  • Description of many-body states with second quantisation.
Most of this is discussed in a summer school lecture I gave several years ago. 

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