# Abelian-symmetric 1-site C4v iPEPS¶

Specialized class for iPEPS with single abelian-symmetric on-site tensor possesing a (C4v) symmetry with respect to the permutation of its auxilliary indices

$a_{suldr} = e^{i\theta} a_{s\textrm{p}(uldr)},$

where $$\textrm{p}$$ is a permutation associated to the symmetries of square lattice: rotations by $$\pi/2$$ and reflections. This property in turn implies ($$A_1$$) symmetry for the double-layer tensor $$A_{(uu')(ll')(dd')(rr')}=a_{suldr}a_{su'l'd'r'}$$.