Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice

TL;DR

This paper explores the quantum phase diagram of the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice, revealing how quantum fluctuations and long-range interactions influence various ordered phases and phase transitions.

Contribution

It introduces an effective quantum dimer model at low fields, analyzes order-by-disorder mechanisms, and discusses potential experimental realizations in Rydberg atom quantum simulators.

Findings

Identification of columnar and clock-ordered phases at low and intermediate fields.

Observation of a 3d-XY quantum phase transition to the polarized phase.

Long-range interactions favor certain ground states, aiding experimental realization.

Abstract

We investigate the quantum phase diagram of the $J_1$-$J_2$-$J_3$ antiferromagnetic transverse-field Ising model on the ruby lattice. In the low-field limit we derive an effective quantum dimer model, analyzing how the extensive ground-state degeneracy at zero field is lifted by an order-by-disorder scenario. We support our analysis by studying the gap-closing of the high-field phase using series expansions. For $J_2>J_3$, we find a columnar phase at low fields, followed by a clock-ordered phase stabilized by resonating plaquettes at intermediate field values, and an emergent 3d-XY quantum phase transition to the polarized high-field phase. For $J_3>J_2$, an order-by-disorder mechanism stabilizes a distinct $k=(0,0)$ order and a quantum phase transition in the 3d-Ising universality class is observed. Further, we discuss the possible implementation of the columnar- and clock-ordered phase in existing Rydberg atom quantum simulators. When taking into account the full algebraically decaying long-range interactions on the ruby lattice, we find that long-range interactions favor the same ground state as the quantum fluctuations induced by a transverse field, which could make the ruby lattice a promising candidate for the realization of a clock-ordered phase.