Topological terms on topological defects: A quantum Monte Carlo study
Topological terms on topological defects: A quantum Monte Carlo study
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DOI：
10.1103/physrevb.104.l161105
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发表时间：
2020-05
影响因子：
3.7
通讯作者：
Toshihiro Sato;M. Hohenadler;T. Grover;J. McGreevy;F. Assaad
中科院分区：
文献类型：
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作者：
Toshihiro Sato;M. Hohenadler;T. Grover;J. McGreevy;F. Assaad
狄拉克费米子在$2+1$维动态生成的反对易SO（3）反铁磁（AFM）和Z $2 $凯库勒价键固体（KVBS）质量映射到场论的拓扑$\theta$-项。这个术语提供了一种机制，用于在不同的破缺态之间进行连续的相变：一个相的拓扑缺陷携带另一个相的电荷，并在相变处增殖。$\theta$-term意味着Z$_2$ KVBS序参量的畴壁包含自旋为1/2$的海森堡链，如$\theta$-term为$\theta = \pi$的$1+1$维SO（3）非线性σ模型所描述的。利用钉扎场来稳定畴壁，我们证明了我们的量子Monte Carlo模拟确实支持在Z$_2$拓扑缺陷处出现自旋为1/2$的链。这个概念可以推广到更高的维度，其中具有拓扑项的2 +1维SO（4）或SO（5）理论在域壁实现。
Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekule valence-bond solid (KVBS) masses map onto a field theory with a topological $\theta$-term. This term provides a mechanism for continuous phase transitions between different symmetry-broken states: topological defects of one phase carry the charge of the other and proliferate at the transition. The $\theta$-term implies that a domain wall of the Z$_2$ KVBS order parameter harbors a spin-$1/2$ Heisenberg chain, as described by a $1+1$ dimensional SO(3) non-linear sigma model with $\theta$-term at $\theta = \pi$. Using pinning fields to stabilize the domain wall, we show that our auxiliary-field quantum Monte Carlo simulations indeed support the emergence of a spin-$1/2$ chain at the Z$_2$ topological defect. This concept can be generalized to higher dimensions where $2+1$ dimensional SO(4) or SO(5) theories with topological terms are realized at a domain wall.