Emergent Physics From Lattice Models of Higher Gauge Theory

A Research Project Grant, funded by the Leverhulme Trust .


Participants:
  • Dr. João Faria Martins (PI);
  • Prof. Paul Purdon Martin (co-I);
  • Prof. Jiannis Pachos (member of the steering committee);
  • and Dr. Celeste Damiani (reserch fellow funded by the Leverhulme Trust).
  • Post-doc position now open at Leeds: Closing Date: Tuesday 29 May 2018
    Research Fellow in Geometric Topology, Topological Quantum Field Theory and Applications to Quantum Computing,


    Our project aim is to investigate the different types of point-like and loop / string-like topologically excited states arising in higher gauge theory lattice models for (3+1)-dimensional topological phases of matter, categorifying Kitaev quantum double model for (2+1)-dimensional topological phases. A central topic of this project concerns analysing the behaviour of loop excitations when they move in three-dimensional space, braid and interact, and explore applications to topological quantum computing and to knot theory in four dimensions.

    Keywords:

    • TQFTs; • Extended TQFTs; • Knotted Surfaces; • Loop Braid Group and Necklace Braid Group; • 2-group; • Crossed Module; • Higher Gauge Theory; • Categorification; • Topological Quantum Computing; • Braided Fusion Category.

    Some relevant publications: