(adsbygoogle = window.adsbygoogle || []).push({}); Checkerboard decomposition???

I need help from guys working with Quantum Monte Carlo. I'm reading about worldline method applied to Heisenberg chain (or nearest-neighbor Hubbard model) and after calculation of nonzero matrix elements I'm immediately thrown to the checkerboard representation of worldline. I've read bunch of papers and books on QMC and in every single one author instantly jumps from matrix elements to the checkerboard representation. Now I don't know is that so obvious that it doesn't require any explanation and I'm just plainly stupid or there's something else, but i would really appreciate if someone would break it down for me into simple steps.

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# Checkerboard decomposition?

Can you offer guidance or do you also need help?

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