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

• URL: http://arxiv.org/abs/2312.12941v2
• Date: Mon, 13 May 2024 15:36:39 GMT
• Title: Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice
• Authors: A. Duft, J. A. Koziol, P. Adelhardt, M. Mühlhauser, K. P. Schmidt,
• Abstract summary: We investigate the quantum phase diagram of the $J_1$-$J$-$J_3$ 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 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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