Ludwig Maximilian University of Munich
The notion of spontaneous symmetry breaking plays a vital role in modern physics. It has been intensively applied in many fields to explore physical laws and to search for new states of matter. However, an obvious aspect has often been overlooked: a symmetry can spontaneously break down to any of its subgroups. Each of these subgroups corresponds to phases with distinctive long range orders. In this talk, I will attempt to give a perspective onto the great diversity of orientational phases by breaking O(n) symmetries, and discuss their relevance to both hard and soft condensed matter systems. This task actually exceeds the reach of standard Ginzburg-Landau theory, while lattice gauge theory is utilized. We will see how the latter can be adopted as a productive tool for classifying the tensor order parameter of those phases and studying the associated phase transitions, highlighting the relation between symmetries and fluctuations. Moreover, it also reveals a chiral liquid phase that is reminiscent of recent observations of experiments on crystal melting.
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