论文标题
结和非热带乐队
Knots and Non-Hermitian Bloch Bands
论文作者
论文摘要
结在量子物理学中具有扭曲的历史。它们被放弃为原子模型失败。直到很久以后，在发现的拓扑量子场理论中，结中的结与威尔逊循环之间的联系。在这里，我们表明，由特征力琴弦绑扎的结提供了具有可分离带的一维非富米（NH）汉密尔顿人的完整拓扑分类。事实证明，A $ \ Mathbb {Z} _2 $结，全球生物培训浆果$ Q $作为Wilson Loop Eigenphass的总和，被证明等于NH频段的置换率。我们显示了以不同的打结为特征的两个阶段之间的过渡，并有两种类型。我们进一步开发了一种算法来为任何所需的结构建相应的紧密结合NH Hamiltonian，并提出了一种通过量子淬灭来探测结结构的方案。该理论和算法由模型的汉密尔顿人证明，例如HOPF链接，Trefoil结，图8结和Whitehead Link。
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that knots tied by the eigenenergy strings provide a complete topological classification of one-dimensional non-Hermitian (NH) Hamiltonians with separable bands. A $\mathbb{Z}_2$ knot invariant, the global biorthogonal Berry phase $Q$ as the sum of the Wilson loop eigenphases, is proved to be equal to the permutation parity of the NH bands. We show the transition between two phases characterized by distinct knots occur through exceptional points and come in two types. We further develop an algorithm to construct the corresponding tight-binding NH Hamiltonian for any desired knot, and propose a scheme to probe the knot structure via quantum quench. The theory and algorithm are demonstrated by model Hamiltonians that feature for example the Hopf link, the trefoil knot, the figure-8 knot and the Whitehead link.
