arXiv 2406.017872024-06-03hep-thcond-mat.str-el

拓扑绝缘体表面上2+1维费米子的玻色化

Bosonization of 2+1 dimensional fermions on the surface of topological insulators

Andrea Cappelli, Lorenzo Maffi, Riccardo Villa

备注：: 48 pages, 3 figures

AI总结：

本文提出在拓扑绝缘体表面利用包含体拓扑BF项和表面项的loop model实现2+1维无质量费米子的玻色化，通过推广的Wilson线描述费米子孤子谱，并规范one-form $Z_2$对称性将其映射回包含自旋扇区与时间反演对称性的费米子理论。

摘要：

三维拓扑绝缘体可以由包含两个“流体力学”Abelian规范场的有效场论来描述。该作用量包含一个体拓扑BF项和一个表面项，称为loop model。这描述了无质量的2+1维激发，并为它们提供了半经典但非平庸的共形不变动力学。鉴于拓扑绝缘体原本是费米子，这种物理设定非常适合用规范场来实现无质量费米子的玻色化。基于对loop model的早期分析，我们发现费米子属于孤子谱，并可以通过1+1维顶点算符的推广由Wilson线来描述。它们的关联函数与共形不变性一致。随后，利用文献中描述的费米子拓扑相的一般构造，将玻色子loop model映射为费米子理论。这需要识别玻色子理论的特征性one-form $Z_2$对称性并对其进行规范，由此产生费米子数$(-1)^F$、自旋扇区以及满足${\cal T}^2=(-1)^F$的时间反演对称性。这些结果在几何$S^2\times S^1$上的有效作用量和配分函数中得到了详细说明。

英文摘要：

Three-dimensional topological insulators can be described by an effective field theory involving two `hydrodynamic' Abelian gauge fields. The action contains a bulk topological BF term and a surface term, called loop model. This describes the massless 2+1 dimensional excitations and provides them with a semiclassical, yet non-trivial conformal invariant dynamics. Given that topological insulators are originally fermionic, this physical setting is ideal for realizing the bosonization of massless fermions in terms of gauge fields. Building on earlier analyses of the loop model, we find that fermions belong to the solitonic spectrum and can be described by Wilson lines, through the generalization of 1+1 dimensional vertex operators. Their correlation functions agree with conformal invariance. The bosonic loop model is then mapped into a fermionic theory by using the general construction of fermionic topological phases described in the literature. It requires the identification of the characteristic one-form $Z_2$ symmetry of the bosonic theory and its gauging, which originates the fermion number $(-1)^F$, the spin sectors and the time reversal symmetry obeying ${\cal T}^2=(-1)^F$. These results are detailed for the effective action and the partition function on the geometry $S^2\times S^1$.

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