You seem to be answering your own question. Obviously there is far too much information to represent in a reasonably sized 2d or 3d plot, so no matter what you do, you will be losing something. If you want a plot that shows correlations between particles, you can do just that: For a spinchain of N sites, create a N×N image, where the value of the pixel at each point (i,j) is given by the expectation value of the operator σAiσBj, where σA/Bi/j∈{σX,σY,σZ}. This gives you 9 possible plots.
It seems likely that you may only care about the case where σA=σB, in which case there are only 3 plots, and you could take the expectation values for XX, YY and ZZ as the R, G and B values for a colour plot.
This kind of thing produces things very similar to the type of plot you have in your question.
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