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We introduce a numerical linked cluster expansion for square-lattice modelswhose building block is an L-shape cluster. For the spin-1/2 models studied inthis work, we find that this expansion exhibits a similar or better convergenceof the bare sums than that of the (larger) square-shaped clusters, and can beused with resummation techniques (like the site- and bond-based expansions) toobtain results at even lower temperatures. We compare the performance of weak-and strong-embedding versions of this expansion in various spin-1/2 models, andshow that the strong-embedding version is preferable because of its convergenceproperties and lower computational cost. Finally, we show that the expansionbased on the L-shape cluster can be naturally used to study properties oflattice models that smoothly connect the square and triangular latticegeometries.

L-based numerical linked cluster expansion for square lattice models