论文标题
拓扑缺陷的拓扑术语：量子蒙特卡洛研究
Topological terms on topological defects: a quantum Monte Carlo study
论文作者
论文摘要
$ 2+1 $尺寸的Dirac Fermions具有动态生成的抗强制性SO（3）反铁磁（AFM）和Z $ _2 $ _2 $kekuléValence-bond solid（KVBS）群众群众映射具有拓扑$θ$ - term的现场理论。该术语为不同对称性破裂状态之间的连续相变提供了一种机制：一个相的拓扑缺陷带有另一个相位的电荷并在过渡时增殖。 $θ$ -Term意味着z $ _2 $ _2 $ kvbs订单参数的域墙既有旋转$ 1/2 $ heisenberg链，如$ 1+1 $ dimensional so（3）非线性Sigma模型，其$θ$ -Term in $θ=π$。使用固定字段来稳定域墙，我们表明我们的辅助场量子蒙特卡洛模拟确实支持了在z $ _2 $拓扑缺陷处的旋转$ 1/2 $链的出现。这个概念可以推广到更高的维度，其中$ 2+1 $尺寸的尺寸（4）左右（5）具有拓扑术语的理论在域墙上实现。
Dirac fermions in $2+1$ dimensions with dynamically generated anticommuting SO(3) antiferromagnetic (AFM) and Z$_2$ Kekulé valence-bond solid (KVBS) masses map onto a field theory with a topological $θ$-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 $θ$-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 $θ$-term at $θ= π$. 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.
