论文标题
使用拓扑不变性的计算相互作用的费米对称性保护拓扑阶段的分类
Computing classification of interacting fermionic symmetry-protected topological phases using topological invariants
论文作者
论文摘要
近年来，通过使用广义的共同体学理论，在对称性保护拓扑（SPT）阶段的分类方面取得了巨大成功。但是，由于计算障碍函数的难度，对广义的共同体学理论的明确计算非常困难。在本文中，基于同型代数中拓扑不变和数学技术的物理图片，我们开发了一种算法来解决这个难题。众所周知，用来列举SPT阶段的对称群的同谋的联合可以在不同的线性碱基（称为分辨率）中等效地表示。通过以减少的分辨率表达双线管的依据，其基础要比以前的研究中常用的选择要少得多，从而大大降低了计算成本。特别是，它降低了无限离散对称组（如壁纸组和空间组）的计算成本。作为示例，我们计算所有17个壁纸对称组
In recent years, great success has been achieved on the classification of symmetry-protected topological (SPT) phases for interacting fermion systems by using generalized cohomology theory. However, the explicit calculation of generalized cohomology theory is extremely hard due to the difficulty of computing obstruction functions. In this paper, based on the physical picture of topological invariants and mathematical techniques in homotopy algebra, we develop an algorithm to resolve this hard problem. It is well known that cochains in the cohomology of the symmetry group, which are used to enumerate the SPT phases, can be expressed equivalently in different linear bases, known as the resolutions. By expressing the cochains in a reduced resolution containing much fewer basis than the choice commonly used in previous studies, the computational cost is drastically reduced. In particular, it reduces the computational cost for infinite discrete symmetry groups, like the wallpaper groups and space groups, from infinity to finity. As examples, we compute the classification of two-dimensional interacting fermionic SPT phases, for all 17 wallpaper symmetry groups
