标题： 二维空间中一种尺度不变态的纠缠熵及其扩展：通用有限尺寸标度 显示英文标题

标题： Entanglement entropy for a type of scale-invariant states in two spatial dimensions and beyond: universal finite-size scaling

摘要： 一种通用方案被提出，用于研究一类尺度不变态的纠缠熵，在二维及更高空间维度中，适用于发生自发对称性破缺并具有类型-B戈德斯通模的量子多体系统基态子空间中的正交基态。 认为纠缠熵的面积定律贡献是不存在的，因为由于简并基态波函数的单元格关于排列对称群的出现，子系统与其环境之间的边界接近程度并不明确。 三个物理约束导致了在纠缠熵的主要对数贡献中的普适有限系统尺寸标度函数。 结果揭示了基态子空间下的抽象分形，其特征是分形维数。 后者与正交基态的类型-B戈德斯通模的数量相同。 该预测在 ${\rm SU}(2)$ 自旋-$s$ 的铁磁海森堡模型、${\rm SU}(2s+1)$ 铁磁模型以及交错的${\rm SU}(3)$ 自旋-1 铁磁双二次模型中得到了数值确认。 显示英文摘要

摘要： A generic scheme is proposed to investigate the entanglement entropy for a type of scale-invariant states, valid for orthonormal basis states in the ground state subspace of quantum many-body systems undergoing spontaneous symmetry breaking with type-B Goldstone modes in two spatial dimensions and beyond. It is argued that a contribution from the area law to the entanglement entropy is absent, since the closeness to the boundary between a subsystem and its environment is not well-defined, given that a permutation symmetry group with respect to the unit cells of degenerate ground state wave functions emerges. Three physical constraints imposed lead to a universal finite-system size scaling function in the dominant logarithmic contribution to the entanglement entropy. As a result, an abstract fractal underlying the ground state subspace is revealed, characterized by the fractal dimension. The latter in turn is identical to the number of type-B Goldstone modes for the orthonormal basis states. The prediction is numerically confirmed for the ${\rm SU}(2)$ spin-$s$ ferromagnetic Heisenberg model, the ${\rm SU}(2s+1)$ ferromagnetic model, and the staggered ${\rm SU}(3)$ spin-1 ferromagnetic biquadratic model.