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The goal of condensed matter physics is to understand the various states of matter. States of matter are characterized by the presence of order: a ferromagnet becomes ordered below the transition temperature. In the Landau-Ginzburg theory ... , order is associated with spontaneous symmetry breaking, described naturally with group theory. Girvin and MacDonald first noted that the order in Hall fluids does not really fit into the Landau-Ginzburg scheme: We have not broken any obvious symmetry. The topological property of the Hall fluids provides a clue to what is going on. As explained in the preceding chapter, the ground state degeneracy of a Hall fluid depends on the topology of the manifold it lives on, a dependence group theory is incapable of accounting for. Wen has forcefully emphasized that the study of topological order, or more generally quantum order, may open up a vast new vista on the possible states of matter. (en) |
