A quantum leap in computing
The quantum world is a bizarre place that often exhibits phenomena that are counter intuitive. Superconductivity, when certain materials possess exactly zero electrical resistance below certain temperatures, is a prime example of such peculiar behaviour. Understanding and describing phenomena at the quantum level requires sophisticated mathematical models and complex equations. However, many of these, such as the Bardeen-Cooper-Schrieffer (BCS) mean field theory of superconductivity, provide only approximations of reality. BCS describes superconductivity as a microscopic effect caused by a 'condensation' of pairs of electrons into a boson-like state. To study more complicated quantum correlations, researchers must resort to methods that go beyond the mean field. One promising candidate is the Richardson-Gaudin (RG) models, which provides mathematical equations that can be solved exactly. However, this is a cumbersome process due to the resulting singularities that occur and explains why the RG models have failed to attract the attention they deserve. The 'New computational tools for the modelling of correlations in quantum systems' (Quantum Modelling) project sought to use insights from exactly solvable models, such as RG, to improve the accuracy of quantum Monte Carlo (QMC) methods for the modelling of correlated quantum systems. These include ultra-cold atomic gases, nuclear matter and non-conventional superconductors. Named after the famous casino, QMC is a large class of computer algorithms that simulate quantum systems in order to solve the quantum many-body problem. One of the project's main breakthroughs was the development of a computer code that can solve the RG equations efficiently even for thousands of particles. This paved the way for the use of RG models to analyse correlations in quantum systems, particularly ultra-small metallic grains, atomic nuclei and p-wave superconductors. The RG equations describe quantum correlations under the ideal condition of zero absolute temperature. They also describe pair correlations in atomic nuclei. In order to maximise Quantum Modelling's scientific utility and impact, the researchers involved also planned to release the computer code under an open source licence.
