Magnetization plateaus of the quantum pyrochlore Heisenberg antiferromagnet

We predict magnetization plateaus ground states for $S=1/2$ Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck–like criterion at finite external magnetic field, enabling the prediction of plateaus in the magnetization versus field diagram. We also develop an analysis based on the spin-parity operator, leading to a condition from which identical predictions are obtained of magnetization plateaus ground states. Both analyses are based on the non-local nature of the transformations, and rely only on the symmetries of the Hamiltonian. This suggests that the plateaus ground states can possess properties arising from non-local entanglement between the spins.

Figure 1

Schematic diagram of the pyrochlore lattice with the basis vectors ${\widehat{a}}_1,{\widehat{a}}_2$, and ${\widehat{a}}_3$ (defined in the main text). Red spheres represent sites with spin $S=1/2$. The four vertices of a tetrahedron are different from one another with respect to their environment, indicating four sub-lattices through the indices $a,b,c$, and $d$. The dashed lines form a tetrahedron, signaling the geometric frustration present in the system.