Full Configuration Interaction Quantum Monte Carlo: from Molecules to Materials

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The fundamental equation governing the properties of atoms, molecules and materials is the many-electron Schr\ odinger equation, whose solution gives the energy of the system under consideration, by solving for the correlated motions of the constituent electrons. Accounting for this correlation has proven to be both essential for useful modelling of materials, as well as extremely difficult to calculate. In this proposal, we will develop a radically new approach to this problem based an algorithm which propagates an evolving distribution of walkers which inhabit an abstract space of states (Slater determinants) which are able to account for this correlation.The algorithm is a remarkably simple set of rules (but specially devised), akin to a Game of Life. This algorithm has been shown by the PI to work efficiently for isolated molecules, extending the range of FCI-level calculations by many orders of magnitude. The proposal here is to extend FCIQMC for an infinitely repeating system, which can be used to model a material such as diamond or graphite. This extension requires the method to be extended in a fundamental way, to allow for complex rather than purely real walkers. A method to do this is proposed in the Case for Support. If successful, this method could transform the field of modelling of materials, in that it would give access, for the first time, a way to compute the correlation energy without the imposition of uncontrolled approximations. In developing experience with this new technique, we hope one day to be able to solve some of the problems posed by the rapidly developing field of correlated materials, which have so far proven impervious to existing methods.