# Chiral Operator and Correlations

I want to calculate the correlation \langle \chi_m \chi_n \rangle where \chi =

Here, i,j,k are the three vertices of a triangle on a triangular lattice ; m,n are the centers of two triangles, and S is the total spin operator.

How can I code this operator and more importantly, how can I calculate the correlation.
I couldn’t find any cross product function and there seems to be too many variables in calculating the correlation.