Non-abelian holonomies in a generalized Lieb lattice

Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping. To this end we consider a generalized photonic Lieb lattice having two degenerate non-dispersive modes and show that, when the lattice parameters are slowly modulated, the photons propagation bears the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control, paving the way to the generation and detection of non-abelian gauge fields in photonic lattices. As shown in Fig. 1 , the lattice, with four sites per unit cell, has two dangling bonds in each cell. The inter- and intra- cell hopping amplitudes are J b 1 and J b 2 while J c and J d denote the hopping along the dangling bonds.