Magnetisation plateaux of the quantum pyrochlore Heisenberg antiferromagnet

Abstract

We predict magnetisation plateaux 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 (OYA)-like criterion at finite external magnetic field, enabling the prediction of plateaux in the magnetisation versus field diagram. We also develop an analysis based on the spinparity operator, leading to a condition from which identical predictions are obtained of magnetisation plateaux 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 plateaux ground states can possess properties arising from non-local entanglement between the spins. We also demonstrate that while a spin-lattice coupling stabilises plateaux in a system of quantum spins with antiferromagnetic exchange, it can compete with weak ferromagnetic spin exchange in leading to frustration-induced magnetisation plateaux.

Comment on arxiv:1902.06475v1, "Magnetisation plateaus of the quantum pyrochlore Heisenberg antiferromagnet"

“…This is naturally a subset of Q p m =16 plateaus mentioned in Ref. 4. The notable case is Q p m = 12, where one needs N 2 or N 3 to be a multiple of 3.…”

“…Some reflection then tells us that these states indeed get captured for Q p m = 12 (not noted in Ref. 4). This is a tripling of the pyrochlore unit cell, as is to be expected since in Ref.…”

“…Recently, the arguments of Refs. 1, 2 were applied to the Kagome 3 and pyrochlore 4 quantum Heisenberg antiferromagnets. The main new ingredient was appropriate twist operators 5 for these highly frustrated magnets that took into account the unit cell geometry.…”