论文标题
带有对称保护边缘的无间隙手性液体
Gapless chirality liquid with symmetry-protected edge spins
论文作者
论文摘要
我们报告说，Spin-1/2四面体海森堡链实现了一个无骨对称性保护的拓扑（GSPT）相，其特征是由于自由度而导致的自由度的chirations tomonaga-luttinger-luttinger-liquid关键性，因此由于自由度而产生的对称性边缘状态。这个GSPT阶段具有一个有趣的功能，没有对称性禁止琐碎的自旋差距开口，而是离散的对称性，$ \ mathbb z_3 \ times \ times \ mathbb z_2^t $，禁止了独特的间隙接地状态。在本文的第一部分中，我们从数值上显示了基于密度 - 矩阵恢复范围的密度重新归一化组（DMRG）方法的临界纠缠熵和非动词堕落的纠缠频谱的共存。我们澄清了自由度的自由度，同时又是自由度的自由度。最后但并非最不重要的一点是，我们使用本地$ \ mathbb {z} _3 $ rotation讨论了GSPT阶段中的Lieb-Schultz-Mattis型配置。因此，我们可以将我们的GSPT阶段描述为受对称保护的临界阶段，该相位受$ \ Mathbb {z} _3 $ on site Symmetry，$ \ mathbb {z} _2^t $ time-time ververs-versemmetraly，lattice transemetry，lattice transmertry，u（1）u（1）对称对称性。
We report that a spin-1/2 tetrahedral Heisenberg chain realizes a gapless symmetry-protected topological (gSPT) phase characterized by the coexistence of the Tomonaga-Luttinger-liquid criticality due to chirality degrees of freedom and the symmetry-protected edge state due to spin degrees of freedom. This gSPT phase has an interesting feature that no symmetry forbids the trivial spin gap opening but a discrete symmetry, $\mathbb Z_3\times\mathbb Z_2^T$, forbids the unique gapped ground state. In the first part of the paper, we numerically show the coexistence of a critical entanglement entropy and a nontrivially degenerate entanglement spectrum based on the density-matrix renormalization group (DMRG) method.Next, we clarify that chirality degrees of freedom form the Tomonaga-Luttinger liquid while spin degrees of freedom form the spin-1 Haldane state based on a degenerate perturbation theory. Last but not least, we discuss the Lieb-Schultz-Mattis-type ingappability in the gSPT phase, using a local $\mathbb{Z}_3$ rotation. We can thus characterize our gSPT phase as a symmetry-protected critical phase protected by the $\mathbb{Z}_3$ on-site symmetry, the $\mathbb{Z}_2^T$ time-reversal symmetry, the lattice translation symmetry, and the U(1) spin-rotation symmetry.
