Menezes Natália, Palumbo Giandomenico, Morais Smith Cristiane
Institute for Theoretical Physics, Center for Extreme Matter and Emergent Phenomena, Utrecht University, Princetonplein 5, 3584, CC, Utrecht, The Netherlands.
Sci Rep. 2017 Oct 26;7(1):14175. doi: 10.1038/s41598-017-14635-y.
It has been shown that local four-fermion interactions on the edges of two-dimensional time-reversal-invariant topological insulators give rise to a new non-Fermi-liquid phase, called helical Luttinger liquid (HLL). Here, we provide a first-principle derivation of this HLL based on the gauge-theory approach. We start by considering massless Dirac fermions confined on the one-dimensional boundary of the topological insulator and interacting through a three-dimensional quantum dynamical electromagnetic field. Within these assumptions, through a dimensional-reduction procedure, we derive the effective 1 + 1-dimensional interacting fermionic theory and reveal its underlying gauge theory. In the low-energy regime, the gauge theory that describes the edge states is given by a conformal quantum electrodynamics (CQED), which can be mapped exactly into a HLL with a Luttinger parameter and a renormalized Fermi velocity that depend on the value of the fine-structure constant α.
研究表明，二维时间反演不变拓扑绝缘体边缘的局域四费米子相互作用会产生一种新的非费米液体相，称为螺旋卢廷格液体（HLL）。在此，我们基于规范理论方法对这种HLL进行了第一性原理推导。我们首先考虑限制在拓扑绝缘体一维边界上且通过三维量子动态电磁场相互作用的无质量狄拉克费米子。在这些假设下，通过降维过程，我们推导出了有效的1 + 1维相互作用费米子理论，并揭示了其 underlying规范理论。在低能区，描述边缘态的规范理论由共形量子电动力学（CQED）给出，它可以精确映射到一个具有依赖于精细结构常数α值的卢廷格参数和重整化费米速度的HLL。
