Quantum frustration and criticality as new regimes of quantum matter

Electrons in solids do not behave independently of one another but correlate their motion to avoid the large repulsive Coulomb forces. Under certain conditions correlation effects can become very strong and lead to completely new properties for the material as a whole. An example is superconductivity with very important technological applications. Here electrical current flows with no resistance, an emergent quantum property of all electrons in the system acting together in unison. A major challenge of current research is to identify the key conditions under which electrons spontaneously organize themselves in such surprisingly robust ways and to determine the quantum rules that govern this behaviour. The research proposed here aims to obtain direct microscopic information about the internal structure and dynamics of unexplored quantum phases of electrons, in particular novel magnetic quantum phases. The research will exploit recent opportunities for high-resolution studies of electronic correlations opened up by new advances in neutron and x-ray instrumentation technology. A central issue of correlated systems is the physics at critical points separating different forms of electronic order. This will be explored experimentally by applying high magnetic fields to an Ising magnet to suppress the transition temperature to spontaneous magnetic order all the way down to zero temperature and thus drive the electrons into a new regime of critical quantum matter on the verge of order with unexplored properties. Here thermal fluctuations are absent but spins fluctuate strongly because of the Heisenberg uncertainty principle with the remarkable property that all ~10^23 spins fluctuate in unison as a single macroscopic quantum state. The energy spectrum of spin fluctuations at the critical point will be measured to compare with current theories of criticality in quantum matter. Of fundamental interest is the behaviour of electrons confined to lattices with strong geometric frustration effects, as realized for triangular layers where no spin arrangement can simultaneously satisfy all antiferromagnetic interactions between nearest neighbours; here many arrangements have comparable energies and quantum fluctuations become very important and can stabilize novel types of quantum order or quasiparticles. This problem of quantum frustration will be explored in a number of insulating and metallic frustrated quantum magnets.