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

TL;DR

This paper investigates a disordered quantum spin-ice model on the pyrochlore lattice, revealing phase transitions from a quantum spin-ice to a spin-glass and a resonating-hexagon phase, with implications for rare-earth pyrochlores.

Contribution

It introduces a new effective spin model with randomness and ring exchanges, analyzing phase transitions and entanglement properties using exact diagonalization.

Findings

Identifies a quantum spin-ice phase with entanglement entropy ln(6).

Discovers a spin-glass phase with long-range order and entanglement entropy ln(2).

Finds a resonating-hexagon phase with a broad entanglement entropy distribution.

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.