Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
Gapless symmetry-protected topological phase of quantum antiferromagnets on anisotropic triangular strip
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DOI：
10.1103/physrevb.106.144436
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发表时间：
2022-05
影响因子：
3.7
通讯作者：
Yuichiro Hidaka;S. Furuya;Atsushi Ueda;Y. Tada
中科院分区：
文献类型：
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作者：
Yuichiro Hidaka;S. Furuya;Atsushi Ueda;Y. Tada
我们研究了具有几何阻挫相互作用的三腿自旋1/2阶梯。我们称这个模型为各向异性三角带（ATS）模型。数值计算和场论表明，它的基态属于一个无间隙的拓扑保护（SPT）相。数值方法是基于密度矩阵重整化群分析的纠缠熵和纠缠谱。而纠缠熵表现出临界行为，纠缠谱是非平凡简并的。这些纠缠性质意味着基态是一个无隙的拓扑相位。我们研究ATS模型使用量子场论来支持数值结果。当链间相互作用被视为作用于三条自旋链的扰动时，链间相互作用几乎将第二条自旋链与其他两条自旋链隔离。然而，同时，第二链介导第一链和第三链之间的铁磁相互作用。因此，ATS模型的基态是一个无隙Tomonaga-Luttinger液体弱耦合到自旋为1的Haldrons链与无关的相互作用。最后但并非最不重要的，我们表明，无间隙SPT阶段的ATS模型是一个安全保护的关键阶段。我们指出，临界对称性的保护是必不可少的无间隙SPT相的表征。
We study a three-leg spin-1/2 ladder with geometrically frustrated interleg interactions. We call this model an anisotropic triangular-strip (ATS) model. We numerically and field-theoretically show that its ground state belongs to a gapless symmetry-protected topological (SPT) phase. The numerical approach is based on density-matrix renormalization group analyses of the entanglement entropy and the entanglement spectrum. Whereas the entanglement entropy exhibits a critical behavior, the entanglement spectrum is nontrivially degenerate. These entanglement properties imply that the ground state is a gapless topological phase. We investigate the ATS model using a quantum field theory to support the numerical findings. When the frustrated interchain interaction is deemed a perturbation acting on the three spin chains, the frustrated interchain interaction almost isolates the second chain from the other two chains. However, at the same time, the second chain mediates a ferromagnetic interaction between the first and third chains. Therefore, the ground state of the ATS model is a gapless Tomonaga-Luttinger liquid weakly coupled to a spin-1 Haldane chain with irrelevant interactions. Last but not least, we show that the gapless SPT phase of the ATS model is a symmetry-protected critical phase. We point out that the symmetry protection of criticality is essential in characterization of the gapless SPT phase.