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Quantum liquid crystals are strongly correlated quantum many-body systems with broken rotational symmetry but with partial or complete translational symmetry. Inspired by the classical theory for hexatic liquid crystals, which deals with the thermal unbinding of dislocations in 2D solids, the present work advances the idea that 3D solids can melt quantum mechanically via unbinding, or rather Bose-Einstein condensation, of dislocation worldsheets, resulting in quantum analogs of nematic, smectic, and columnar liquid crystals. In these phases, the phonons, as represented by two-form dual gauge fields, develop a mass gap reflecting the loss of shear rigidity.
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Beekman et al. (2017) studied this question.
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