双层量子自旋液体中的磁性碎裂与分数化Goldstone模式
Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
AI总结：
研究了正方晶格上双层量子自旋液体模型的相图，发现其低能极限由具有增强SO(4)对称性的π-flux Hubbard模型描述，反铁磁Mott转变引发磁性碎裂，伴随分数化且非局域的Goldstone玻色子。
摘要：
我们研究了在正方晶格上具有Kitaev型相互作用的双层量子自旋液体模型的相图。我们表明，低能极限由具有增强SO(4)对称性的π-flux Hubbard模型描述。Hubbard模型的反铁磁Mott转变标志着双层自旋和轨道自由度的磁性碎裂转变。碎裂的“Néel order”除了各向异性局域序参量外，还具有面内Néel分量的非局域弦序参量。当Néel矢量沿ẑ方向时，相关的量子序由演生的Z2×Z2规范场表征，否则由Z2规范场表征。我们用微扰计算支持了这些结果，这与场论分析一致。最后讨论了这些相的低能集体激发，并表明Z2×Z2相的Goldstone玻色子是分数化且非局域的。
英文摘要：
We study the phase diagram of a bilayer quantum spin liquid model with Kitaev-type interactions on a square lattice. We show that the low energy limit is described by a $π$-flux Hubbard model with an enhanced SO(4) symmetry. The antiferromagnetic Mott transition of the Hubbard model signals a magnetic fragmentation transition for the spin and orbital degrees of freedom of the bilayer. The fragmented "Néel order" features a non-local string order parameter for an in-plane Néel component, in addition to an anisotropic local order parameter. The associated quantum order is characterized by an emergent $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ gauge field when the Néel vector is along the $\hat{z}$ direction, and a $\mathbb{Z}_2$ gauge field otherwise. We underpin these results with a perturbative calculation, which is consistent with the field theory analysis. We conclude with a discussion on the low energy collective excitations of these phases and show that the Goldstone boson of the $\mathbb{Z}_{2} \times \mathbb{Z}_{2}$ phase is fractionalized and non-local.
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