论文标题
1+1维相互作用的费米子系统中的全身泵
Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
论文作者
论文摘要
无泵是一种现象，其中$ \ mathrm {u}（1）$电荷从费米子系统的边缘泵送到另一个边缘。无用的泵已在各个维度和各种电荷中被概括。在本文中，我们调查了$ 1+1 $维相互作用的费米尼短距离（SRE）状态的琐事和非平凡阶段中的普通泵。为此，我们使用矩阵产品状态（MPSS）。 MPS以$ 1+1 $尺寸描述多体系统，并且可以以代数为代数。我们证明了Fermionic MPS（FMPSS）的基本定理，并使用它们来研究广义的TH泵。我们在微不足道和非平凡的阶段构建非平凡的泵，并显示泵与相互作用的稳定性。此外，我们在FMPS方面定义了通用泵的拓扑不变性，并与现有结果建立一致性。这些是SRE国家家族的不变，而不是被较高维度的浆果曲率捕获的。我们还争论了一般性泵的拓扑不变性与$ k $ - 理论在Donovan-Karoubi配方中的扭曲之间的关系。
The Thouless pump is a phenomenon in which $\mathrm{U}(1)$ charges are pumped from an edge of a fermionic system to another edge. The Thouless pump has been generalized in various dimensions and for various charges. In this paper, we investigate the generalized Thouless pumps of fermion parity in both trivial and non-trivial phases of $1+1$-dimensional interacting fermionic short range entangled (SRE) states. For this purpose, we use matrix product states (MPSs). MPSs describe many-body systems in $1+1$ dimensions, and can characterize SRE states algebraically. We prove fundamental theorems for fermionic MPSs (fMPSs) and use them to investigate the generalized Thouless pumps. We construct non-trivial pumps in both the trivial and non-trivial phases and we show the stability of the pumps against interactions. Furthermore, we define topological invariants for the generalized Thouless pumps in terms of fMPSs and establish consistency with existing results. These are invariants of the family of SRE states that are not captured by the higher dimensional Berry curvature. We also argue a relation between the topological invariants of the generalized Thouless pump and the twist of the $K$-theory in the Donovan-Karoubi formulation.
