College of Science & Engineering
The discovery of high-temperature superconductors (of both the cuprate and oxypnictide classes, for example) has been accompanied by an enormous surge of interest in the study of quantum spin systems, particularly in two dimensions. Many theoretical and experimental investigations have attempted to probe possible links between the mechanisms of high-temperature superconductivity in the cuprate materials and spin fluctuations and magnetic order in 2D spin-1/2 (and spin-1) antiferromagnets. This research program centers on applying the coupled cluster method (CCM) to a large and diverse array of 2D quantum spin systems of theoretical and experimental interest, particularly those involving strong frustration, that are difficult to treat by other methods. The interesting magnetic phenomena displayed by such systems also makes them suitable candidates for many technological applications. The nature of the paramagnetic or nonmagnetic phases without long-range magnetic order in some quantum antiferromagnets has particularly attracted a great deal of interest too, in the hope of tracing their possible association with the mechanism of high-temperature superconductivity. Indeed, more generally, the whole subject of (zero-temperature) quantum phase transitions in frustrated quantum magnets has become an extremely active and fast-moving topic in recent years. The CCM is now widely accepted as being one of the most successful and most widely applicable of all modern methods of microscopic quantum many-body theory. The CCM techniques pioneered by this group are probably now the best available for these strongly frustrated 2D quantum spin-lattice systems, and their results are now setting the benchmarks in the field. These researchers are also very interested in the longer term to extend the existing zero-temperature formalism to finite temperatures, in order to investigate the effects of thermal fluctuations on quantum phase transitions. If successful this will open up a whole new research area of huge interest to both the statistical physics and condensed-matter communities.