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We investigate finite-size scaling of genuine multisite entanglement in theground state of quantum spin-1/2 Heisenberg ladders. We obtain the groundstates of odd- and even-legged Heisenberg ladder Hamiltonians and computegenuine multisite entanglement, the generalized geometric measure (GGM), whichshows that for even rungs, GGM increases for odd-legged ladder while itdecreases for even ones. Interestingly, the ground state obtained byshort-range dimer coverings, under the resonating valence bond (RVB) ansatz,encapsulates the qualitative features of GGM for both the ladders. We find thatwhile the GGMs for higher legged odd- and even-ladders converge to a singlevalue in the asymptotic limit of a large number of rungs, the finite-sizescaling exponents of the same tend to diverge. The scaling exponent of GGMobtained by employing density matrix recursion method is therefore a reliablequantity in distinguishing the odd-even dichotomy in Heisenberg ladders, evenwhen the corresponding multisite entanglements merge.

Diverging scaling with converging multisite entanglement in odd and even quantum Heisenberg ladders