Spin- 12 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalization study

We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze 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 ${J}₁={J}₂$.