论文标题
可解决的晶格哈密顿的分数厅电导率和自旋-C结构
Fractional Hall Conductivity and Spin-c Structure in Solvable Lattice Hamiltonians
论文作者
论文摘要
Kapustin-Fidkowski No-Go定理禁止$ u（1）$对称拓扑订单，在（2+1）d中以（2+1）d的非平凡霍尔电导率接纳通勤投影仪的汉密尔顿人，后者是后者是构造拓扑订单的范围可解决的晶格模型的范式方法。即使拓扑命令本质上承认投影仪哈密顿量的通勤命令，该定理也禁止使用$ u（1）$全球对称性的相互作用，该对称会产生霍尔电导率。尽管如此，在这项工作中，我们表明，对于所有（2+1）d $ u（1）$对称的Abelian拓扑顺序，我们可以构建一个可以在低能量下可控制的晶格汉密尔顿，即使不是完全可以解决的”；因此，这种无关定理并没有导致对这些拓扑秩序的晶格研究造成重大困难。此外，对于我们的构造中的费米子拓扑命令，我们介绍了旋转-C结构的晶格概念 - 在连续体中，这一概念以前在晶格环境中没有充分引入。
The Kapustin-Fidkowski no-go theorem forbids $U(1)$ symmetric topological orders with non-trivial Hall conductivity in (2+1)d from admitting commuting projector Hamiltonians, where the latter is the paradigmatic method to construct exactly solvable lattice models for topological orders. Even if a topological order would intrinsically have admitted commuting projector Hamiltonians, the theorem forbids so once its interplay with $U(1)$ global symmetry which generates Hall conductivity is taken into consideration. Nonetheless, in this work, we show that for all (2+1)d $U(1)$ symmetric abelian topological orders of such kind, we can construct a lattice Hamiltonian that is controllably solvable at low energies, even though not "exactly" solvable; hence, this no-go theorem does not lead to significant difficulty in the lattice study of these topological orders. Moreover, for the fermionic topological orders in our construction, we introduce the lattice notion of spin-c structure -- a concept important in the continuum that has previously not been adequately introduced in the lattice context.
