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 orientation
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 $J_1 = J_2$.

Reference : V. R. Chandra and J. Sahoo, arXiv:1710.11316