Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model

Abstract

We study an effective spin model derived perturbatively from random transverse-field Ising model on the pyrochlore lattice. The model consists of spin-configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization upto N=64 site systems. We calculate spin-glass correlation functions and local entanglement entropy $S_T$ between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where $S_T=\ln 6$. Increasing randomness first leads to a frozen phase, with long-range spin-glass order and $S_T=\ln 2$ corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.

arXiv comment6 pages and 7 figures

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• The magnetic behaviour of Dy${}_2$Ir${}_2$O${}_7$ -- beyond the mean field approximation
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