All spin-1 topological phases in a single spin-2 chain
All spin-1 topological phases in a single spin-2 chain
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DOI：
10.1103/physrevb.91.205118
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发表时间：
2014-12
影响因子：
3.7
通讯作者：
A. Kshetrimayum;Hong-Hao Tu;R. Orús
中科院分区：
文献类型：
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作者：
A. Kshetrimayum;Hong-Hao Tu;R. Orús
在这里，我们研究的出现不同的对称性保护拓扑（SPT）阶段的自旋2量子链。我们考虑一个具有双线性、双二次、双三次和双四次最近邻相互作用以及单轴各向异性的类海森堡模型。我们证明了该模型包含四种不同的有效自旋1 SPT相，对应于$（\mathbb{Z}_2 \times \mathbb {Z}_2）+ T$对称群的不同表示，其中$\mathbb{Z}_2$是自旋内部空间中的某种$\pi$旋转，$T$是时间反演的.其中一个相相当于通常的自旋1的Haldom相，而其他三个是不同的，但也是典型的自旋1系统。该模型还表现出$SO（5）$-Haldrons相。此外，我们还发现不同有效自旋-1 SPT相之间的跃迁是连续的，并且可以用c=2的共形场论来描述。在这样的过渡，间接证据表明，可能的有效场理论的四个无质量马约拉纳费米子。通过无限时间演化块抽取方法，以及有效场论的考虑，通过使用矩阵乘积状态在热力学极限中近似系统的基态得到结果。我们的研究结果表明，第一次，不同的大有效自旋-1 SPT相分离的连续量子相变可以稳定在一个简单的量子自旋链。
Here we study the emergence of different Symmetry-Protected Topological (SPT) phases in a spin-2 quantum chain. We consider a Heisenberg-like model with bilinear, biquadratic, bicubic, and biquartic nearest-neighbor interactions, as well as uniaxial anisotropy. We show that this model contains four different effective spin-1 SPT phases, corresponding to different representations of the $(\mathbb{Z}_2 \times \mathbb{Z}_2) + T$ symmetry group, where $\mathbb{Z}_2$ is some $\pi$-rotation in the spin internal space and $T$ is time-reversal. One of these phases is equivalent to the usual spin-1 Haldane phase, while the other three are different but also typical of spin-1 systems. The model also exhibits an $SO(5)$-Haldane phase. Moreover, we also find that the transitions between the different effective spin-1 SPT phases are continuous, and can be described by a $c=2$ conformal field theory. At such transitions, indirect evidence suggests a possible effective field theory of four massless Majorana fermions. The results are obtained by approximating the ground state of the system in the thermodynamic limit using Matrix Product States via the infinite Time Evolving Block Decimation method, as well as by effective field theory considerations. Our findings show, for the first time, that different large effective spin-1 SPT phases separated by continuous quantum phase transitions can be stabilized in a simple quantum spin chain.