Generalized Thouless pumps in (1+1)-dimensional interacting fermionic systems

Background The Thouless pump is a phenomenon in which U(1) electric charges are pumped from an edge of a system to another edge. The Thouless pump was originally proposed for a system in 1+1 dimension. However, it is known that such a pumping phenomenon exists in various dimensions. There are also many variations on the charge to be pumped, such as a model in which the fermion parity is pumped instead of the U(1) charge. These are collectively called generalized Thouless pumps. Such a pumping phenomenon is considered to be a general phenomenon for systems described by Short Range Entangled (SRE) states. These results, however, are for a system without interaction, and the stability of the system with interaction and the quantities that characterize the pump phenomenon are not known.

Method and Result We analyze the pump phenomenon in (1+1)-dimensional systems using fermionic matrix product states (fMPS), which is a method to represent many-body quantum states by a set of matrices. By using fMPS, a SRE state can be characterized by the algebraic properties (Z/2Z-graded central simplicity). We define topological invariants of pumps by using Z/2Z-graded central simple fMPS and confirm the stability of pump with interactions. Using this invariant, we propose a novel system with a fermion parity pump. In addition, we pointed out that mathematically this invariant is related to a quantity called twist of K-theory. This led us to discuss the geometric meaning of topological pump.

Summary

- We proposed a new topological invariant which detect a fermion parity pump.

- We made some interacting models which has a non-trivial fermion parity pump.

- We have clarified the geometric meaning of the pump invariants.