发表机构
Pontificia Universidad Católica de Chile（智利天主教 Pontificia 大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过磁相干态框架构造了朗道哈密顿量的渐近拟局部结构，建立了离散-连续词典，为将Lieb-Robinson型技术推广到连续磁场电子系统奠定基础。
AI 中文摘要
我们引入了一个磁相干态框架，覆盖二维朗道哈密顿量的朗道能级，该框架由一个结合空间和能量自由度的离散度量空间索引。尽管该框架是过完备的，但它几乎是正交的，我们利用它赋予单粒子希尔伯特空间上的CAR $C^*$--代数一个渐近拟局部（AQL）结构，在该结构中，位于不相交索引集上的可观测量的分级交换子呈指数衰减而非精确消失。通过一族到由此产生的局部子代数的条件期望，我们构造了一个几乎局部可观测量的Fréchet $*$--子代数，该子代数在格点平移的离散群作用下不变，且该群通过连续自同构作用于其上。对于完整的磁平移连续群，我们建立了关于局部可观测量如何在该几乎局部代数中传播的定量控制，并证明该控制足以将分级渐近交换性从格点扩展到整个连续平移群。这些结果提供了一个离散-连续词典，旨在作为将Lieb-Robinson型技术从格点系统扩展到磁场中相互作用的连续电子的起点。
英文摘要
We introduce a magnetic coherent--state frame over the Landau levels of the two--dimensional Landau Hamiltonian, indexed by a discrete metric space combining spatial and energy degrees of freedom. Although overcomplete, the frame is almost--orthogonal, and we use it to endow the CAR $C^*$--algebra over the one--particle Hilbert space with an \emph{asymptotic quasi--local} (AQL) structure, in which graded commutators of observables localized on disjoint index sets decay exponentially rather than vanish exactly. By means of a family of conditional expectations onto the resulting local subalgebras, we construct a Fréchet $*$--subalgebra of almost--local observables, invariant under the discrete group of lattice translations, which act on it by continuous automorphisms. For the full continuous group of magnetic translations we establish a quantitative control on how local observables spread through this almost--local algebra, and we show that this control suffices to extend graded asymptotic abelianness from the lattice to the entire continuous translation group. The results provide a discrete--continuum dictionary intended as the starting point for extending Lieb--Robinson--type techniques from lattice systems to interacting continuum electrons in a magnetic field.
Comments67 pages. Keywords: Landau Hamiltonian, magnetic frame, CAR $C^*$--algebra, asymptotic quasi--locality, asymptotic abelianness
