Arttu Rajantie

Defect Formation in Quantum Phase Transitions

Phase transitions, such as the change of water to ice, can often be characterised by ideas of symmetry and symmetry breaking. In the case of the water/ice transition, the water is unchanged by rotations because the water molecules are disordered. When the temperature of the water is lowered the water molecules become ordered as the water changes into ice. Ordered structures have preferred directions and so the rotational symmetry is broken once in the ice phase. The idea of symmetry breaking is very general and can also be used to describe quantum phase transitions, which occur when the parameters of quantum systems are changed.

When a symmetry breaking transition occurs, the system in question must choose how to order itself. However, well separated regions cannot know which ordering one another are choosing at the time. Therefore, after the transition, the system will in fact consist of a patchwork of orderings, rather than a single uniform one. The boundaries where different orderings meet are called defects. Such objects are well conserved because the whole system needs to be rearranged to get rid of them. Once again, we can apply the same arguments to quantum phase transitions which must therefore, form defects.

 Since defects are well conserved, they can be observed even long times after formation. This means they should also be observable in quantum systems that have undergone some equilibration or even decoherence. This is interesting because the dynamics of the phase transition gets imprinted on the defects via their spatial distribution. This means one could, by observing defects, learn about the otherwise unknowable quantum dynamics that led to their formation, whether this be in many-body quantum systems of cold atoms or in the early universe itself.