Shapourian Hassan, Shiozaki Ken, Ryu Shinsei
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
Phys Rev Lett. 2017 May 26;118(21):216402. doi: 10.1103/PhysRevLett.118.216402. Epub 2017 May 25.
We define and compute many-body topological invariants of interacting fermionic symmetry-protected topological phases, protected by an orientation-reversing symmetry, such as time-reversal or reflection symmetry. The topological invariants are given by partition functions obtained by a path integral on unoriented spacetime which, as we show, can be computed for a given ground state wave function by considering a nonlocal operation, "partial" reflection or transpose. As an application of our scheme, we study the Z_{8} and Z_{16} classification of topological superconductors in one and three dimensions.
我们定义并计算了相互作用的费米子对称性保护拓扑相的多体拓扑不变量，这些拓扑相由时间反演或反射对称等反向对称性保护。拓扑不变量由在无定向时空上通过路径积分得到的配分函数给出，正如我们所展示的，对于给定的基态波函数，可以通过考虑一种非局部操作，即“部分”反射或转置来计算。作为我们方案的一个应用，我们研究了一维和三维拓扑超导体的(Z_{8})和(Z_{16})分类。
