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

TL;DR

This study uses exact diagonalisation to analyze the quantum properties of the spin-1/2 antiferromagnet on the pyrochlore lattice, revealing rapid decay of correlations and the role of tetrahedral triplet states in the ground state.

Contribution

First exact diagonalisation analysis of the breathing pyrochlore system across different coupling regimes, highlighting the evolution of correlations and entanglement.

Findings

Rapid decay of spin correlations

Presence of multiple singlet excitations below magnetic gap

Significant tetrahedral triplet contribution to ground state entanglement

Abstract

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 $J_1 = J_2$.