论文标题
价键固体，遗迹顺序和二维量子磁铁中的SO（5）对称性
Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
论文作者
论文摘要
我们在2D方格上引入了具有多体相关的海森堡型相互作用的量子自旋1/2模型，该模型旨在托管Plaquette Valence-bond固体（PVBS）基态断裂$ \ MATHBB {Z} _4 _4 $对称性。我们对抗铁磁（AFM）和PVBS状态之间的量子相跃迁进行了详细的量子蒙特卡洛研究。我们发现了一阶转变，与先前研究的AFM和柱状价键固体之间的连续“解抗”转变相反。我们表明，AFM-PVBS转变处的共存状态意外地与SO（5）对称性相关联，这可能表明过渡连接到解义的临界点。我们还讨论了在PVBS状态中具有Fracton特性的最新提案中的一阶转变，得出的结论是不可能的。此外，我们发现了一种新型的八倍变化VBS相的类型，它破坏了PVBS阶段的剩余$ \ Mathbb {z} _2 $对称性。然后可以将PVB阶段视为中间的“残留”阶段，我们开发了一种一般的图理论方法来描述两阶段离散的对称性破坏。在有限温度下，我们观察到波动引起的一阶转变，这是残留相变的标志。我们还提到了与高t $ _ {\ rm c} $超导性的SO（5）理论的可能连接。
We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the 2D square lattice, designed to host a plaquette valence-bond solid (PVBS) ground state breaking $\mathbb{Z}_4$ symmetry. We carry out a detailed quantum Monte Carlo study of the quantum phase transition between the antiferromagnetic (AFM) and PVBS states. We find a first-order transition, in contrast to previously studied continuous 'deconfined' transitions between the AFM and columnar valence-bond solids. We show that the coexistence state at the AFM--PVBS transition is unexpectedly associated with SO(5) symmetry, which may indicate that the transition is connected to a deconfined critical point. We also discuss the first-order transition in the context of a recent proposal of spinons with fracton properties in the PVBS state, concluding that the fracton scenario is unlikely. Further, we discover a novel type of eight-fold degenerate VBS phase that breaks the remaining $\mathbb{Z}_2$ symmetry of the PVBS phase. The PVBS phase can then be regarded as an intermediate 'vestigial' phase, and we develop a general graph-theoretic approach to describe the two-stage discrete symmetry breaking. At finite temperature, we observe fluctuation-induced first-order transitions, which are hallmarks of vestigial phase transitions. We also mention possible connections to the SO(5) theory of high-T$_{\rm c}$ superconductivity.
