标题： 自旋晶格海森堡反铁磁体中的对称性破缺和竞争的价键态 显示英文标题

标题： Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet

摘要： 我们使用无限投影纠缠对态（iPEPS）和高阶级数展开法研究了自旋-$1/2$交错反铁磁海森堡模型在星形晶格上的基态相图。 该模型包含两种不同的耦合：二聚体键上的$J_d$和三聚体键上的$J_t$。 虽然已知当$J_d \ge J_t$时系统存在单线态固体（VBS）相，但$J_d < J_t$时的基态相图仍未确定。 我们的iPEPS模拟揭示了一个一阶相变发生在$J_d/J_t \approx 0.18$，显著低于之前报告的估计值。 在此转变之后，我们发现两种单线态晶体（VBC）态之间存在紧密竞争：柱状VBC和$\sqrt{3} \times \sqrt{3}$VBC，后者在所有有限的键维下始终表现出更低的能量。 高阶级数展开支持这一结论，发现$\sqrt{3} \times \sqrt{3}$VBC态确实变得在能量上更有利，但仅在微扰理论的六阶时才显现，揭示了候选态之间竞争的微妙性。 显示英文摘要

摘要： 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.