Universal Wave-Function Overlap and Universal Topological Data from Generic Gapped Ground States
We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/97743 https://orcid.org/0000-0002-5874-581X |
| Summary: | We propose a way—universal wave-function overlap—to extract universal topological data from generic ground states of gapped systems in any dimensions. Those extracted topological data might fully characterize the topological orders with a gapped or gapless boundary. For nonchiral topological orders in (2+1)D, these universal topological data consist of two matrices S and T, which generate a projective representation of SL(2,Z) on the degenerate ground state Hilbert space on a torus. For topological orders with a gapped boundary in higher dimensions, these data constitute a projective representation of the mapping class group MCG(M[superscript d]) of closed spatial manifold M[superscript d]. For a set of simple models and perturbations in two dimensions, we show that these quantities are protected to all orders in perturbation theory. These overlaps provide a much more powerful alternative to the topological entanglement entropy and allow for more efficient numerical implementations. |
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