Symmetry-protected topological phases and competing orders in a spin-1/2
Symmetry-protected topological phases and competing orders in a spin-1/2
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自旋 1/2 中对称保护的拓扑相和竞争阶
DOI：
10.1103/physrevb.104.075135
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发表时间：
2021
影响因子：
3.7
通讯作者：
Kawashima Naoki
中科院分区：
文献类型：
--
作者：
Ogino Takuhiro;Furukawa Shunsuke;Kaneko Ryui;Morita Satoshi;Kawashima Naoki
本文研究了一个在两条腿的梯子上具有四自旋相互作用的自旋XXZ模型。通过有效场理论和矩阵积态计算，我们得到了由八个不同的带隙相组成的丰富的基态相图。其中四个表现出自发的对称性破缺与磁性或价键固体（VBS）的长程有序。其他四个是没有特色的，即，体基态是唯一的并且不破坏任何对称性。无特征相包括梯级单线态（RS）和Haldleman相以及它们的变体，RS* 和Haldleman * 相，其中两条腿之间形成扭曲单线态对。我们论证了中心电荷的高斯跃迁发生在无特征相和有序相之间，而中心电荷的伊辛跃迁发生在无特征相和有序相之间。这两种跃迁线相交于对称点，在对称点处的临界性用Wess-Zumino-维滕理论描述。RS-Half * 和RS*-Half * 跃迁给出了拓扑相变的例子。有趣的是，具有高度各向异性性质的RS* 和Halfenite * 相甚至出现在各向同性情况的附近。我们证明，所有四个无特征的阶段是由拓扑指数在某些对称性的存在下区分。
We study a spin-XXZ model with a four-spin interaction on a two-leg ladder. By means of effective field theory and matrix product state calculations, we obtain rich ground-state phase diagrams that consist of eight distinct gapped phases. Four of them exhibit spontaneous symmetry breaking with either a magnetic or valence-bond-solid (VBS) long-range order. The other four are featureless, i.e., the bulk ground state is unique and does not break any symmetry. The featureless phases include the rung singlet (RS) and Haldane phases as well as their variants, the RS* and Haldane* phases, in which twisted singlet pairsare formed between the two legs. We argue and demonstrate that Gaussian transitions with the central chargeoccur between the featureless phases and between the ordered phases while Ising transitions withoccur between the featureless and ordered phases. The two types of transition lines cross at the-symmetric point, where the criticality is described by theWess-Zumino-Witten theory with. The RS-Haldane* and RS*-Haldane transitions give examples of topological phase transitions. Interestingly, the RS* and Haldane* phases, which have highly anisotropic nature, appear even in the vicinity of the isotropic case. We demonstrate that all the four featureless phases are distinguished by topological indices in the presence of certain symmetries.