Non-abelian Quantum Statistics on Graphs

Tomasz Maciążek, Adam Sawicki

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)
111 Downloads (Pure)

Abstract

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.

Original languageEnglish
Pages (from-to)921-973
Number of pages53
JournalCommunications in Mathematical Physics
Volume371
Issue number3
Early online date9 Oct 2019
DOIs
Publication statusPublished - 1 Nov 2019

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