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

The Thouless pump is a phenomenon in which 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 nontrivial 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 nontrivial pumps in both the trivial and nontrivial 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.

Automated summary

This paper investigates the generalized Thouless pumps in (1+1)-dimensional interacting fermionic systems. By using matrix product states to describe the systems, the authors construct nontrivial pumps in both trivial and nontrivial phases and prove their stability against interactions. Furthermore, topological invariants for the pumps are defined and shown to be consistent with existing results, providing a characterization of the SRE states that is not captured by higher dimensional Berry curvature.