The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study

We present exact diagonalisation calculations for the spin-1/2 nearest neighbour antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the $[111]$ direction and analyse the Hamiltonian of the breathing pyrochlore system with two coupling constants $J_1$ and $J_2$ for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra ($J_2 = 0$) to a correlated state at $J_1=J_2$. We evaluate the low energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near $J_1=J_2$ to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground state entanglement at $J_1 = J_2$.