Quantum Liquid Crystals

This title encapsulates a theoretical research program that has been going on since twenty years or so in Zaanen’s group. This started in the late 1990’s; Emery, Kivelson and Fradkin had introduced the idea that quantum incarnations of liquid crystalline order may exist. In the intervening years this has become a mainstream subject, becoming clear that these are found in a variety of strongly correlated electron systems such as the cuprates and Iron pnictides (see e.g. [149]). Zaanen’s interest was in the universal description of the long wavelength physics of such order doing justice to the strong coupling nature of the microscopic physics. In other words, what is the strongly coupled effective quantum field theoretical description? The template is the mighty vortex-boson duality dealing with a simple complex scalar (superfluid) I”. n 2+1 Dimensions. Although this was explored in the 1970’s for the topological melting of crystals in two classical dimensions by Nelson-Halperin-Kosterlitz-Thouless-Young, identifying the hexatic liquid crystal as dislocation condensate, it was never attempted to generalize this to the quantum case. Zaanen bumped into the work by Hagen Kleinert

who had in the 1980’s laid down a powerful mathematical repertoire to deal with such higher dimensional duality structures associated with elasticity. Rooted in the non-Abelian and semidirect structure of the Poincare group describing the nature of space, this forms an amazingly rich affair. Despite the familiarity of solids, this “Field theoretic elasticity” appears to be the most fanciful field theoretical structure that may cross the path of a condensed matter physicist.

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