期刊
NATIONAL SCIENCE REVIEW
卷 3, 期 1, 页码 68-106出版社
OXFORD UNIV PRESS
DOI: 10.1093/nsr/nwv077
关键词
quantum matter; topological order; long range entanglement; modular tensor category
资金
- NSF [DMR-1005541]
- NSFC [11274192]
- John Templeton Foundation [39901]
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1005541] Funding Source: National Science Foundation
In primary school, we were told that there are four phases of matter: solid, liquid, gas, and plasma. In college, we learned that there are much more than four phases of matter, such as hundreds of crystal phases, liquid crystal phases, ferromagnet, anti-ferromagnet, superfluid, etc. Those phases of matter are so rich, it is amazing that they can be understood systematically by the symmetry breaking theory of Landau. However, there are even more interesting phases of matter that are beyond Landau symmetry breaking theory. In this paper, we review new 'topological' phenomena, such as topological degeneracy, that reveal the existence of those new zero-temperature phase-topologically ordered phases. Microscopically, topologically orders are originated from the patterns of long-range entanglement in the ground states. As a truly new type of order and a truly new kind of phenomena, topological order and long-range entanglement require a new language and a new mathematical framework, such as unitary fusion category and modular tensor category to describe them. In this paper, we will describe a simple mathematical framework based on measurable quantities of topological orders (S, T, c) proposed around 1989. The framework allows us to systematically describe all 2+1D bosonic topological orders (i.e. topological orders in local bosonic/spin/qubit systems).
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