Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
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| Format: | Preprint |
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2025
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| _version_ | 1866917148026208256 |
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| author | Ghosh, Pratyay Koziol, Jan Nyckees, Samuel Schmidt, Kai Phillip Mila, Frédéric |
| author_facet | Ghosh, Pratyay Koziol, Jan Nyckees, Samuel Schmidt, Kai Phillip Mila, Frédéric |
| contents | We investigate the ground state phase diagram of the spin-$1/2$ antiferromagnetic Heisenberg model on the star lattice using infinite projected entangled pair states (iPEPS) and high-order series expansions. The model includes two distinct couplings: $J_d$ on the dimer bonds and $J_t$ on the trimer bonds. While it is established that the system hosts a valence bond solid (VBS) phase for $J_d \ge J_t$, the ground state phase diagram for $J_d < J_t$ has remained unsettled. Our iPEPS simulations uncover a first-order phase transition at $J_d/J_t \approx 0.18$, significantly lower than previously reported estimates. Beyond this transition, we identify a close competition between two valence bond crystal (VBC) states: a columnar VBC and a $\sqrt{3} \times \sqrt{3}$ VBC, with the latter consistently exhibiting lower energy across all finite bond dimensions. The high-order series expansion supports this by finding that the $\sqrt{3} \times \sqrt{3}$ VBC state indeed becomes energetically favorable, but only at sixth order in perturbation theory, revealing the subtle nature of the competition between candidate states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_05133 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet Ghosh, Pratyay Koziol, Jan Nyckees, Samuel Schmidt, Kai Phillip Mila, Frédéric Strongly Correlated Electrons We investigate the ground state phase diagram of the spin-$1/2$ antiferromagnetic Heisenberg model on the star lattice using infinite projected entangled pair states (iPEPS) and high-order series expansions. The model includes two distinct couplings: $J_d$ on the dimer bonds and $J_t$ on the trimer bonds. While it is established that the system hosts a valence bond solid (VBS) phase for $J_d \ge J_t$, the ground state phase diagram for $J_d < J_t$ has remained unsettled. Our iPEPS simulations uncover a first-order phase transition at $J_d/J_t \approx 0.18$, significantly lower than previously reported estimates. Beyond this transition, we identify a close competition between two valence bond crystal (VBC) states: a columnar VBC and a $\sqrt{3} \times \sqrt{3}$ VBC, with the latter consistently exhibiting lower energy across all finite bond dimensions. The high-order series expansion supports this by finding that the $\sqrt{3} \times \sqrt{3}$ VBC state indeed becomes energetically favorable, but only at sixth order in perturbation theory, revealing the subtle nature of the competition between candidate states. |
| title | Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2508.05133 |