Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916242432983040 |
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| author | Duft, A. Koziol, J. A. Adelhardt, P. Mühlhauser, M. Schmidt, K. P. |
| author_facet | Duft, A. Koziol, J. A. Adelhardt, P. Mühlhauser, M. Schmidt, K. P. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_12941 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice Duft, A. Koziol, J. A. Adelhardt, P. Mühlhauser, M. Schmidt, K. P. Strongly Correlated Electrons Quantum Gases Quantum Physics 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. |
| title | Order-by-disorder in the antiferromagnetic $J_1$-$J_2$-$J_3$ transverse-field Ising model on the ruby lattice |
| topic | Strongly Correlated Electrons Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2312.12941 |