Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet

Abstract We construct rigorous Anderson-type lower bounds on the ground-state energy of the spin- S Heisenberg antiferromagnet on the pyrochlore lattice. By formulating and optimizing a hierarchy of local cluster motifs ordered by size, we generate a sequence of increasingly tight bounds. A seven-site “hourglass” cluster composed of two corner-sharing tetrahedra furnishes an optimized lower bound that admits a closed-form expression for arbitrary spin S . We also derive rigorous lower bounds for generalized models with further-neighbor exchange, ring exchange, and scalar spin-chirality interactions. For S = 1 2 and S = 1, numerical optimization of an 18-site “crown” cluster containing a hexagonal loop yields rigorous lower bounds on the ground-state energy per site of the nearest-neighbor Heisenberg model with unit exchange, e GS ≥ −0.549832 and e GS ≥ −1.632985, respectively. We compare the resulting bounds with numerical estimates of the ground-state energy from the literature.