论文标题
玻色粒的部分填充$ e_8 $量子厅州
Partial fillings of the bosonic $E_8$ quantum Hall state
论文作者
论文摘要
我们研究了由电子构建的纤维音拓扑阶段。除了散装的激发能隙外，这些骨阶段还具有费米的能量隙，在大批和边缘中的所有局部激发都均为电子组合。我们专注于手性阶段，其中所有低能边缘激发沿相同的方向移动，这是由短程纠缠的$ e_8 $ Quantum Hall State（填充了最低Landau电子水平的波索尼）类似物产生的。 $ e_8 $ edge-state理论具有$ e_8 $ kac-moody对称性，可以分解为$ {\ cal g} _a \ times {\ cal g} _b $ subalgebras，例如$ su（3）\ times e_6 $，$ sO（m）$ sO（m）\ so（m）\ so（m）$ so（16-m）$ g_ $ g_4 $ $ g_4 $ \ $ f。 （在这里，$ \ {so（m）\} $，$ \ {su（n）\} $，以及$ \ {e_8，g_2，f_4 \} $表示正交，单一和异常的lie代数。 g} _a $或$ {\ cal g} _b $ bosonic分数量子大厅指出``部分填充$ e_8 $ state''状态，并且与广义的粒子孔对称性相关。这些远程纠缠的状态具有亚伯利亚或非亚伯利亚拓扑序列。 fibonacci Anyons，以及缩合的$ \ Mathbb {z} _2 $量规通量和电荷。
We study bosonic topological phases constructed from electrons. In addition to a bulk excitation energy gap, these bosonic phases also have a fermion energy gap, below which all local excitations in the bulk and on the edge are even combinations of electrons. We focus on chiral phases, in which all low-energy edge excitations move in the same direction, that arise from the short-range entangled $E_8$ quantum Hall state, the bosonic analog of the filled lowest Landau level of electrons. The $E_8$ edge-state theory features an $E_8$ Kac-Moody symmetry that can be decomposed into ${\cal G}_A \times {\cal G}_B$ subalgebras, such as $SU(3) \times E_6$, $SO(M) \times SO(16-M)$, and $G_2 \times F_4$. (Here, $\{SO(M) \}$, $\{SU(N)\}$, and $\{E_8, G_2, F_4 \}$ denote orthogonal, unitary, and exceptional Lie algebras.) Using these symmetry decompositions, we construct exactly solvable coupled-wire model Hamiltonians for families of long-range entangled ${\cal G}_A$ or ${\cal G}_B$ bosonic fractional quantum Hall states that ``partially fill" the $E_8$ state and are pairwise related by a generalized particle-hole symmetry. These long-range entangled states feature either Abelian or non-Abelian topological order. Some support the emergence of non-local Dirac and Majorana fermions, Ising anyons, metaplectic anyons, Fibonacci anyons, as well as deconfined $\mathbb{Z}_2$ gauge fluxes and charges.
