期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 371, 期 3, 页码 921-973出版社
SPRINGER
DOI: 10.1007/s00220-019-03583-5
关键词
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资金
- National Science Centre of Poland [2015 / 18 / E / ST1 / 00200, 2017 / 24 / T / ST1 / 00489, 2016 / 23 / N / ST1 / 03209]
We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of particles constrained to move in a topological space X. The framework involves a study of isomorphism classes of flat complex vector bundles over the configuration space of X which can be achieved by determining its homology groups. We apply this methodology for configuration spaces of graphs. As a conclusion, we provide families of graphs which are good candidates for studying simple effective models of anyon dynamics as well as models of non-abelian anyons on networks that are used in quantum computing. These conclusions are based on our solution of the so-called universal presentation problem for homology groups of graph configuration spaces for certain families of graphs.
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