30. Conclusions

  • There is no logical reason to say that band theory itself breaks down in some general way in strongly correlated systems.

  • There really is almost no practical difference between electronic structure calculations of weakly and strongly correlated systems. The level of accuracy attainable and the range of properties that can be computed is essentially the same (with the usual caveats about heavier atoms).

  • This is not true if you wish to use the LDA or GGA approximations to density functional theory. The problem with self-interaction means that cases where orbital polarization is important (which tend to be 'strongly correlated') will converge to an incorrect ground state.

  • Various ways to get these materials to approach something like the right ground state are :
    (1) use Hartree-Fock theory (which works much better than you might expect) or
    (2) use DFT hybrid functionals like B3LYP which contain some fraction of the exact non-local HF exchange
    (3) For really accurate calculations - use either of the previous two options as input to a quantum Monte Carlo calculation.

Things to think about

  • Is the Mott insulating state in something like NiO a new state of matter, as sometimes claimed, or is it just a collection of slightly perturbed semi-independent Ni2+ ions?

  • How, if at all, can electronic structure calculations of this kind be of use in collaborating with field theorists/many-body theorists?



So, well, that's about it. I guess my main contention has therefore been to say that actually, there is very little difference between the accuracy of the band theory treatment of strongly and weakly correlated materials, provided you use a reasonable Hamiltonian which treats the relevant interactions properly. Now the correct response to that is, of course, so what? Most things that we don't know about strongly correlated materials are actually beyond the reach of one-electron calculations. But I suppose we do have the advantage that we can easily look at real, rather than model systems, and maybe some of the intuitive ideas that can be provided might prove useful. The full many-body treatment amenable with quantum Monte Carlo could be a good direction to go in the future.