Singlet Excitations in Pyrochlore: A Study of Quantum Frustration

We apply the contractor renormalization (CORE) method to the spin half Heisenberg antiferromagnet on the frustrated checkerboard and pyrochlore lattices. Their ground states are spin-gapped singlets which break lattice symmetry. Their effective Hamiltonians describe fluctuations of orthogonal singlet pairs on tetrahedral blocks, at an emergent low energy scale. We discuss low temperature thermodynamics and new interpretations of finite size numerical data. We argue that our results are common to many models of quantum frustration.

Figure 1

The pyrochlore (a) and checkerboard (b) lattices.

Figure 2

A low energy singlet excitation which is a bound state of two vertical triplets. This state is represented by a single pseudospin flip in the crossed plaquette approach. In contrast, the horizontal triplet pair shown in gray cannot be described by a simple spin flip in this crossed plaquettes basis.

Figure 3

The pyrochlore viewed as a cubic lattice of supertetrahedra. The arrows show the direction of the supertetrahedra’s pseudospin in the mean field ground state.