28. Quantum Monte Carlo

  • QMC allows us to work with the fully correlated many-body wave function, and is capable of extremely high accuracy.

  • With this technique, it is straightforward to calculate, for example, excitation energies that include the relaxation and screening effects that are missing from a consideration of rigid band structures.

  • QMC requires as input a 'trial wave function' generated from a one-electron calculation. Our QMC code CASINO can work with periodic wave functions for crystals as well as with molecules and we can therefore do QMC calculations on strongly correlated solids using e.g. the HF wave functions as a starting guess.



Currently my main area of research is the development of quantum Monte Carlo methods. I'm going to say very little about this, because we haven't actually done any calculations on anything that isn't carbon and silicon so I've got nothing to show you [WEBNOTE: that was two years ago]. I'll merely mention that this is a technique which will allow us to work with the fully correlated many body wave function. You feed it a trial wave function from a one-electron band theory calculation which is then multiplied by a function which depends explicitly on the distances between electrons. We've rewritten our QMC code to take input from the program which has produced all the results you've seen so far, and added some functionality to allow it to compute excited states and to work with multiple determinants.

The point about excitation energies computed with this technique is that we are including something like the screening that we lost by not having any Hartree-Fock correlation, and also the relaxation. When you excite electrons, the orbitals and therefore the density will relax in response to the excitation, which you lose by simply considering the eigenvalues in a rigid band structure.

So this is a promising technique, and if we wanted to we could play with some of the systems that I've been talking about today. Hopefully we'll have more to say on that later in the year.