Herzog-Arbeitman Jonah, Bernevig B Andrei, Song Zhi-Da
Department of Physics, Princeton University, Princeton, NJ, 08544, USA.
Donostia International Physics Center, P. Manuel de Lardizabal 4, 20018, Donostia-San Sebastian, Spain.
Nat Commun. 2024 Feb 8;15(1):1171. doi: 10.1038/s41467-024-45395-9.
The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.
无相互作用费米子的拓扑相已根据其对称性进行了分类，最终形成了一种现代电子能带理论，其中波函数拓扑可从动量空间获得。最近，实空间不变量（RSIs）为全局动量空间指标提供了一种空间局部描述。目前的工作将这种实空间分类推广到相互作用的二维态。我们构造多体局部RSIs作为开放边界上一组对称算符的量子数，但它们与边界的选择无关。利用U(1)粒子数，它们产生多体脆弱拓扑指标，我们用这些指标来确定哪些单粒子脆弱态在弱耦合下是多体拓扑的或平凡的。为此，我们构造了一个具有单粒子脆弱拓扑的精确可解哈密顿量，它通过强耦合绝热地连接到一个平凡态。然后我们在周期性边界条件下定义全局多体RSIs。它们在能带理论极限下简化为陈数，但也能识别出没有单粒子对应物的强关联稳定拓扑相。最后，我们表明多体局部RSIs在描述该相的拓扑量子场论中表现为温 - 泽项的量子化系数。
