拓扑狄拉克半金属的玻色子模拟：有效理论、相邻相和线结构
A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
摘要：
我们构建了一个二维拓扑狄拉克半金属（DSM）的玻色子模拟。最基本的2D DSM模型的低能描述由动量空间中位置$\pm\mathbf{k}_0$的两个狄拉克锥组成。狄拉克锥的局部稳定性由复合对称性$Z_2^{\mathcal{TI}}$保证，其中$\mathcal{T}$是时间反演，$\mathcal{I}$是反演。该模型还表现出有趣的时间反演和反演对称性破缺的电磁响应。在这项工作中，我们构建了一个玻色子的版本，取代每个狄拉克锥的$O(4)$非线性西格玛模型（NLSM）与拓扑θ项和θ角$θ=\pm π$的副本。该NLSM的一个副本还描述了3D Bosonic拓扑绝缘体（BTI）的无间隙表面终止。我们计算的时间反演和反演对称性破缺电磁响应，我们的模型，并表明，它们是在DSM的情况下得到的值的两倍，匹配人们可能期望从，例如，玻色子陈省身绝缘体。我们还研究了BSM模型的稳定性，发现复合$Z_2^{\mathcal{TI}}$对称性再次起着重要的作用。一路上，我们澄清了许多方面的表面理论的BTI，包括电磁响应，电荷和统计的涡旋激发，和稳定性的稳定性，允许扰动。我们简要地评论了本文中使用的$O(4)$ NLSM与$θ=π$的各种描述（双涡旋描述和四个无质量费米子的描述）与最近提出的双描述的BTI表面的$2+1$维量子电动力学与两种费米子（$N=2$ QED $_3$）。在一组四个摘要中，我们回顾了本文中使用的一些工具，并得出了一些更具技术性的结果。
英文摘要：
We construct a bosonic analog of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions $\pm\mathbf{k}_0$ in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry $Z_2^{\mathcal{TI}}$, where $\mathcal{T}$ is time-reversal and $\mathcal{I}$ is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the $O(4)$ Nonlinear Sigma Model (NLSM) with topological theta term and theta angle $θ=\pm π$. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite $Z_2^{\mathcal{TI}}$ symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the $O(4)$ NLSM with $θ=π$ used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of $2+1$ dimensional Quantum Electrodynamics with two flavors of fermion ($N=2$ QED$_3$). In a set of four Appendixes we review some of the tools used in the paper, and also derive some of the more technical results.
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