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Title:
Geometric test for topological states of matter
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Abstract:
We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Wu and Avron-Seiler to the higher-genus surface. We propose this setting as a test to characterise whether the quantum state of matter is "topological" and apply our test to the Laughlin states. We compute the Chern classes of bundles of Laughlin states over the space of Aharonov-Bohm fluxes through the holes of the surface (Laughlin bundles), the degeneracy of the Laughlin states on higher genus Riemann surfaces with any number of quasi-holes, settling the Wen-Niu conjecture, as well as the dimensions of the corresponding Hilbert spaces. We then show that the Laughlin bundles without the localized quasi-holes are not projectively flat. Based on the upcoming paper with D. Zvonkine.
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