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arXiv 1609.02565cond-mat.mes-hallcond-mat.other
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扩大参数空间中的竞争绝热无泵

Competing Adiabatic Thouless Pumps in Enlarged Parameter Spaces

Pedro L. S. Lopes, Pouyan Ghaemi, Shinsei Ryu, Taylor L. Hughes

摘要:

通过哈密顿量的平滑变形,守恒电荷通过绝缘物质的转移被称为量子绝热或无量纲泵浦。这种现象的核心是哈密顿量,其绝缘间隙由多维(通常是二维)参数空间控制,其中可以为哈密顿量中的绝热变化定义路径,即,而不缩小差距。在这里,我们通过考虑一个更大的,三维的参数空间扩展的概念的带状绝缘体的无源泵。我们表明,这个参数空间的连通性是至关重要的定义量子泵,表明,相对于传统的二维情况下,泵浦量不仅取决于初始和最终点的哈密顿演化,但也对类的选择路径和保存的对称性。因此,我们区分了封闭/开放路径的哈密顿演化的情况下,发现不同的封闭周期可以导致不同的量子数的泵,不同的开放路径可能指向不同的表面物理的情况。作为明确的例子,我们考虑的模型类似于简单的模型来描述拓扑绝缘体,但与最小的拓扑绝缘体模型相比,具有两倍的自由度。来自加倍的额外的费米子味道允许额外的间隙项/绝热参数-除了保留拓扑保护离散对称性的通常拓扑质量之外-产生扩大的绝热参数空间。我们认为,在一个和三个\emph{spatial}维的情况下,我们的结果在三维的结晶拓扑绝缘体的背景下,可以实现,我们简要讨论。

英文摘要:

The transfer of conserved charges through insulating matter via smooth deformations of the Hamiltonian is known as quantum adiabatic, or Thouless, pumping. Central to this phenomenon are Hamiltonians whose insulating gap is controlled by a multi-dimensional (usually two-dimensional) parameter space in which paths can be defined for adiabatic changes in the Hamiltonian, i.e., without closing the gap. Here, we extend the concept of Thouless pumps of band insulators by considering a larger, three-dimensional parameter space. We show that the connectivity of this parameter space is crucial for defining quantum pumps, demonstrating that, as opposed to the conventional two-dimensional case, pumped quantities depend not only on the initial and final points of Hamiltonian evolution but also on the class of the chosen path and preserved symmetries. As such, we distinguish the scenarios of closed/open paths of Hamiltonian evolution, finding that different closed cycles can lead to the pumping of different quantum numbers, and that different open paths may point to distinct scenarios for surface physics. As explicit examples, we consider models similar to simple models used to describe topological insulators, but with doubled degrees of freedom compared to a minimal topological insulator model. The extra fermionic flavors from doubling allow for extra gapping terms/adiabatic parameters - besides the usual topological mass which preserves the topology-protecting discrete symmetries - generating an enlarged adiabatic parameter-space. We consider cases in one and three \emph{spatial} dimensions, and our results in three dimensions may be realized in the context of crystalline topological insulators, as we briefly discuss.

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