TY  - JOUR
AU  - Kaufmann, Ralph M.
AU  - Khlebnikov, Sergei
AU  - Wehefritz-Kaufmann, Birgit
TI  - Re-Gauging Groupoid, Symmetries and Degeneracies for Graph Hamiltonians and Applications to the Gyroid Wire Network
JO  - Annales Henri Poincaré
VL  - 17
IS  - 6
SN  - 1424-0661
CY  - Basel
PB  - Birkhäuser
M1  - PUBDB-2018-00564
M1  - DESY-12-133
M1  - arXiv:1208.3266
SP  - 1383 - 1414
PY  - 2016
N1  - (c) Springer Basel
AB  - We study a class of graph Hamiltonians given by a type of quiver representation to which we can associate (non)-commutative geometries. By selecting gauging data, these geometries are realized by matrices through an explicit construction or a Kan extension. We describe the changes in gauge via the action of a re-gauging groupoid. It acts via matrices that give rise to a noncommutative 2-cocycle and hence to a groupoid extension (gerbe). We furthermore show that automorphisms of the underlying graph of the quiver can be lifted to extended symmetry groups of re-gaugings. In the commutative case, we deduce that the extended symmetries act via a projective representation. This yields isotypical decompositions and super-selection rules. We apply these results to the primitive cubic, diamond, gyroid and honeycomb wire networks using representation theory for projective groups and show that all the degeneracies in the spectra are consequences of these enhanced symmetries. This includes the Dirac points of the G(yroid) and the honeycomb systems.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000376288300004
DO  - DOI:10.1007/s00023-015-0443-8
UR  - https://bib-pubdb1.desy.de/record/399259
ER  -