Besides the obvious symmetries global X, Y and Z, there is another symmetry composed of all the Sigmaz on one of the two ladders.
However, with the function I designed for automatically looking for the possible order parameter candidates, I didn't see any new candidates by adding this new symmetry.
I suppose there is some algebraic reason for this result (or even more general cases, i.e., there is no such local operator that commutes with all local symmetries as well as global X and Y but anticommutes with Z_1 and Z_2), but right now I haven't come up with any straightforward proof of it.
Anyway, this is not so important, since we already showed that there is no sign of any existing local order parameter within 8 spin sites.
Besides the obvious symmetries global
X,YandZ, there is another symmetry composed of all theSigmazon one of the two ladders.However, with the function I designed for automatically looking for the possible order parameter candidates, I didn't see any new candidates by adding this new symmetry.
I suppose there is some algebraic reason for this result (or even more general cases, i.e., there is no such local operator that commutes with all local symmetries as well as global
XandYbut anticommutes withZ_1andZ_2), but right now I haven't come up with any straightforward proof of it.Anyway, this is not so important, since we already showed that there is no sign of any existing local order parameter within
8spin sites.