Order-by-disorder in the antiferromagnetic J1-J2-J3 transverse-field Ising model on the ruby lattice

Extensively degenerate ground-state spaces due to frustration pose a formidable resource for emergent quantum phenomena. Perturbing extensively degenerate ground-state spaces may result in several distinct scenarios lifting the ground-state degeneracy. First, an infinitesimal perturbation can lead to a symmetry-broken order (order-by-disorder) or second the perturbation can result in a symmetry-unbroken phase (disorder-by-disorder), which can be either trivial or an exotic quantum spin liquid. Here, we investigate the antiferromagnetic J1-J2-J3 transverse-field Ising model on the ruby lattice by deriving an effective quantum dimer model in the low-field limit and employing high-order series expansions from the high-field limit. We find a columnar order as well as an exotic clock-ordered phase arising from an order-by-disorder mechanism. When taking into account the algebraically decaying long-range interactions on the ruby lattice, we find that long-range interactions favor the same ground state as the quantum fluctuation induced by a transverse field, which could make the ruby lattice a promising candidate for the realization of the clock-ordered phase in existing Rydberg atom quantum simulators.

Pizza and drinks will be served after the seminar in ATL 2117.