Mathematical structure of anyons in planar quantum spin systems

Summary

This application is in mathematical physics. Our research is partly motivated by potential applications in quantum computation. Technically, we propose to study quantum spin systems on infinite two-dimensional lattices. In particular, we plan to develop a framework for describing "charges" or "excitations" in such models. Our main goal is to find - in this quantum spin setting - a suitable analogue of the Doplicher-Haag-Roberts theory of superselection sectors in (algebraic) quantum field theory. This amounts to finding a framework in which single excitations of the spin model can be described by certain linear maps of the observables. The study of such maps should reveal all relevant properties of the excitations, such as what happens if we interchange two excitations ("braiding") or when two excitations are brought close together ("fusion"). Our focus is primarily on models with anyonic excitations, for example Kitaev?s quantum double model or the Levin-Wen string-net model.

Output

Chapter in book

  • P. Naaijkens, R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason(2015): Advances in Algebraic Quantum Field Theory pp. 365 - 395 , Switzerland

Scientific article

Publications for the general public

Details

Project number

680-50-1118

Main applicant

Dr. P. Naaijkens

Affiliated with

Universität Hannover, Institut für Theoretische Physik

Team members

Dr. P. Naaijkens

Duration

01/08/2012 to 16/01/2015