Quantum liquids without symmetry breaking : theories of geometrical phases and their applications

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Quantum liquids are characteristic phases of matter that do no have any fundamental symmetry breaking. Then usually quite successful standard techniques based on order parameters are anymore not effective for the characterization. In order to classify the quantum liquids, we have constructed a theory of material phases using quantum mechanical geometrical phases (Berry connections). We have applied these general theories for concrete quantum systems by calculating the Berry phases and Chern numbers and successfully characterized classically featureless phases clearly.