Emergence: from spins to charges

Emergence is one of the major buzz words of our times – but what does it mean ? Many things to many people is the answer. My working definition, which gives plenty of room for manoeuvre is: the appearance of unexpected many body phenomena, given the symmetries of the Hamiltonian and degrees of freedom at the microscopic level. In this colloquium I will discuss two topical examples in which the quasi-particle excitations of a model spin system with discrete symmetry appear as the topological charges of an emergent electro-magnetic field. In the planar clock model in two dimensions one finds the now famous Kosterlitz-Thouless phase transition which is a confinement – deconfinement transition of emergent electric charge. In the frustrated magnetic material, spin ice the quasi-particles appear to be freely moving magnetic charge – magnetic monopoles – and the system emerges as a magnetic Coulomb fluid in the grand canonical ensemble. With the addition of quantum fluctuations the emergent magneto-statics develops further into a complete analogue of quantum electrodynamics. I will aliment this discussion with experimental results from a wide range of systems.​