论文标题
分形维度和金石模式的计数规则
Fractal dimension and the counting rule of the Goldstone modes
论文作者
论文摘要
有人认为，有一组正统的基础状态，这些状态看起来是高度退化的基础状态，这是由于自发对称性与B型金矿模式的破坏而产生的，并且它们是尺度上不变的，具有显着特征，符合熵$ s（n）$ a（n）$ scale a Googarmanmy scale a $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。事实证明，预制剂是B型Goldstone模式$ N_B $的一半。这是通过对正统基础状态进行精确的施密特分解来实现的，从而在真实空间中揭示了它们的自相似性 - 分形的本质。与现场理论预测结合[O. A. Castro-Alvaredo和B. Doyon，物理。莱特牧师。 \ textbf {108}，120401（2012）]，我们被识别出分形维$ d_f $，其数量是b goldstone模式的数量$ n_b $用于量子多体系统中的正常基础状态。
It is argued that there are a set of orthonormal basis states, which appear as highly degenerate ground states arising from spontaneous symmetry breaking with a type-B Goldstone mode, and they are scale-invariant, with a salient feature that the entanglement entropy $S(n)$ scales logarithmically with the block size $n$ in the thermodynamic limit. As it turns out, the prefactor is half the number of type-B Goldstone modes $N_B$. This is achieved by performing an exact Schmidt decomposition of the orthonormal basis states, thus unveiling their self-similarities in the real space - the essence of a fractal. Combining with a field-theoretic prediction [O. A. Castro-Alvaredo and B. Doyon, Phys. Rev. Lett. \textbf{108}, 120401 (2012)], we are led to the identification of the fractal dimension $d_f$ with the number of type-B Goldstone modes $N_B$ for the orthonormal basis states in quantum many-body systems undergoing spontaneous symmetry breaking.
