Symmetry-protected intermediate trivial phases in quantum spin chains
Symmetry-protected intermediate trivial phases in quantum spin chains
复制标题
量子自旋链中对称保护的中间平凡相
DOI：
10.1103/physrevb.93.245112
复制
发表时间：
2016
影响因子：
3.7
通讯作者：
R. Orus
中科院分区：
文献类型：
--
作者：
A. Kshetrimayum;H.-Hao Tu;R. Orus
物质的对称保护平凡(SPT)相是对称保护拓扑(SPT)相的积态类似物。这意味着，SPT相可以通过某种路径绝热地连接到产物状态，从而保持保护对称性。此外，当在哈密顿量中加入破坏保护SPT有序的对称性的相互作用项时，SPT和SPT相可以绝热地相互连接。量子自旋链中的自旋为1的SPT相可以作为自旋为2的哈密顿量的有效中间相出现。在这篇文章中，我们证明了类似的情况也适用于SPT阶段。更准确地说，对于给定的自旋2量子链，在相图的某些区域出现了有效的中间自旋1 SPT相，这些相也绝热地连接到非平凡的中间SPT相。我们通过研究纠缠熵、与对称性有关的有序参数和单位保真度等量来表征我们模型的相图。我们的数值分析使用矩阵乘积态和无限时间演化的块抽取方法来近似热力学极限下系统的基态。此外，我们还给出了SPT相间可能的量子相变的场论描述。结合数值结果，这种描述表明这种相变可以用有中心电荷的共形场理论来描述。我们的结果与Y.Fuji，F.Pollmann和M.Oshikawa[Phys.莱特牧师。114,177204(2015)PRLTAO0031-900710.1103/PhysRevLett.114.177204].
Symmetry-protected trivial (SPt) phases of matter are the product-state analog of symmetry-protected topological (SPT) phases. This means, SPt phases can be adiabatically connected to a product state by some path that preserves the protecting symmetry. Moreover, SPt and SPT phases can be adiabatically connected to each other when interaction terms that break the symmetries protecting the SPT order are added in the Hamiltonian. It is also known that spin-1 SPT phases in quantum spin chains can emerge as effective intermediate phases of spin-2 Hamiltonians. In this paper we show that a similar scenario is also valid for SPt phases. More precisely, we show that for a given spin-2 quantum chain, effective intermediate spin-1 SPt phases emerge in some regions of the phase diagram, these also being adiabatically connected to nontrivial intermediate SPT phases. We characterize the phase diagram of our model by studying quantities such as the entanglement entropy, symmetry-related order parameters, and 1-site fidelities. Our numerical analysis uses matrix product states and the infinite time evolving block decimation method to approximate ground states of the system in the thermodynamic limit. Moreover, we provide a field theory description of the possible quantum phase transitions between the SPt phases. Together with the numerical results, such a description shows that the transitions may be described by conformal field theories with central charge. Our results are in agreement with, and further generalize, those of Y. Fuji, F. Pollmann, and M. Oshikawa [Phys. Rev. Lett. 114, 177204 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.177204].