论文标题
在Majorana零模式和（2+1）d中的对称和手性的非扰动约束
Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
论文作者
论文摘要
在（1+1）d拓扑阶段中，只有当内部对称组的$ g_f $将基态的内部对称组$ g_f $划分为$ g_f = g_b \ times \ times \ times \ times \ mathbb {z} _2 _2^f $，其中$ g_b {z} _2^f $（$ gathbb {z} _2 f $ pare ferm ferm ferm ferm ferme），才能出现（1+1）d的拓扑阶段。相比之下，即使$ g_f $不是$ g_b \ times \ times \ times \ mathbb {z} _2^f $，（2+1）D拓扑超导体（TSC）即使$ g_f $不为缺陷，也可以在缺陷处托管MZM。在本文中，我们研究了$ g_f $如何与手性中央电荷$ c _- $一起严格限制不配对MZM的存在和对称缺陷的量子数量。我们的结果利用了（2+1）d可逆的费米子拓扑状态的最新代数表征，该状态提供了一种基于拓扑量子场理论的非扰动方法，超出了自由费米子。 We study physically relevant groups such as $\mathrm{U}(1)^f\rtimes H,\mathrm{SU}(2)^f \times H, \mathrm{U}(2)^f\rtimes H $, generic Abelian groups, as well as more general compact Lie groups, antiunitary symmetries and crystalline symmetries.我们提出了一个代数公式，用于费米子晶体等效原理，该公式具有晶体和内部对称性的状态之间的等效性。鉴于我们的理论，我们讨论了先前提出的对TSC材料中未配对MZM的实现，例如SR $ _2 $ ruo $ _4 $，过渡金属二甲植物和铁超导体，其中结晶对称性通常很重要；在某些情况下，我们对这些模型的性质提出了其他预测。
In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b \times \mathbb{Z}_2^f$, where $\mathbb{Z}_2^f$ is generated by fermion parity, $(-1)^F$. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b \times \mathbb{Z}_2^f$. In this paper we study how $G_f$ together with the chiral central charge $c_-$ strongly constrain the existence of unpaired MZMs and the quantum numbers of symmetry defects. Our results utilize a recent algebraic characterization of (2+1)D invertible fermionic topological states, which provides a non-perturbative approach based on topological quantum field theory, beyond free fermions. We study physically relevant groups such as $\mathrm{U}(1)^f\rtimes H,\mathrm{SU}(2)^f \times H, \mathrm{U}(2)^f\rtimes H $, generic Abelian groups, as well as more general compact Lie groups, antiunitary symmetries and crystalline symmetries. We present an algebraic formula for the fermionic crystalline equivalence principle, which gives an equivalence between states with crystalline and internal symmetries. In light of our theory, we discuss several previously proposed realizations of unpaired MZMs in TSC materials such as Sr$_2$RuO$_4$, transition metal dichalcogenides and iron superconductors, in which crystalline symmetries are often important; in some cases we present additional predictions for the properties of these models.
