论文标题
紧急QCD $ _3 $分数Chern绝缘子的量子相变
Emergent QCD$_3$ Quantum Phase Transitions of Fractional Chern Insulators
论文作者
论文摘要
Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely QCD$_3$-Chern-Simons quantum phase transitions of fractional Chern insulators.这些相转换是由Dirac Fermions与非亚伯式Chern-Simons仪表字段（$ u（n）$，$ su（n）$，$ usp（n）$等相互作用的描述。利用Chern-Simons仪表理论和非亚伯党构造的水平二元性，我们讨论了两种类型的QCD $ _3 $量子相变。第一种类型发生在不同的Ja那教序列之间的两个Abelian状态之间，而不是相同的Ja那教序列中的Abelian状态之间的Qed3转变。一个很好的例子是$σ^{xy} = 1/3 $状态与$σ^{xy} = - 1 $状态之间的过渡，它具有$ n_f = 2 $ dirac fermions与$ u（2）$ chern-simons-simons-simons仪表字段相互作用。第二种自然涉及非亚伯国家。为了实验性可行性，我们专注于类似Pfaffian状态的过渡，包括Moore-Read Pfaffian，抗Pfaffian，抗Pfaffian，颗粒 - 孔 - 孔 - 孔 - 孔 - 孔 - 孔 - 孔相变，可以在实验系统中实现，例如诸如石烯元素杂质结构中的分数Chern绝缘子等实验系统。
Motivated by the recent work of QED$_3$-Chern-Simons quantum critical points of fractional Chern insulators (Phys. Rev. X \textbf{8}, 031015, (2018)), we study its non-Abelian generalizations, namely QCD$_3$-Chern-Simons quantum phase transitions of fractional Chern insulators. These phase transitions are described by Dirac fermions interacting with non-Abelian Chern-Simons gauge fields ($U(N)$, $SU(N)$, $USp(N)$, etc.). Utilizing the level-rank duality of Chern-Simons gauge theory and non-Abelian parton constructions, we discuss two types of QCD$_3$ quantum phase transitions. The first type happens between two Abelian states in different Jain sequences, as opposed to the QED3 transitions between Abelian states in the same Jain sequence. A good example is the transition between $σ^{xy}=1/3$ state and $σ^{xy}=-1$ state, which has $N_f=2$ Dirac fermions interacting with a $U(2)$ Chern-Simons gauge field. The second type is naturally involving non-Abelian states. For the sake of experimental feasibility, we focus on transitions of Pfaffian-like states, including the Moore-Read Pfaffian, anti-Pfaffian, particle-hole Pfaffian, etc. These quantum phase transitions could be realized in experimental systems such as fractional Chern insulators in graphene heterostructures.
