We investigate coupled dynamics of spinless fermions on a one-dimensional lattice and spins on the links. When the hopping integral and the on-site potential of the fermions depend on the direction of the link spins, the low-energy effective theory predicts that the link spins behave as a dynamical axion field in 1+1 dimensions. The axion field
θ is coupled to the electric field
E as
θE, through which the link spins rotate in response to the applied electric field or the chemical potential gradient for charge-neutral fermions. This is the inverse phenomenon of Thouless pumping in the Rice-Mele model. After analyzing the dynamics by approximating the link spins with the classical ones and utilizing the axion Lagrangian, we show the full-quantum dynamics using the tensor network method. Even though we do not explicitly introduce the axion Lagrangian in solving the fermion-spin coupled many-body dynamics, the full-quantum results agree well with those with the classical spin approximation, including the dynamics of the axion field and fermion transport. In addition, we find that the quantum correlation between spins accelerates the dynamics of axion fields as the suppression of the expectation values of the link spins allows them to rotate easily. We also propose a possible experimental setup for cold-atomic systems to implement the Hamiltonian in this study.
Abstract The Aharonov-Bohm (AB) effect is an important discovery in quantum theory and electrodynamics. It serves as a surprising quantum phenomenon in which an electrically charged particle can be affected by an electromagnetic potential, despite being confined to a region in which both the magnetic field and electric field are zero. This fact gives the electromagnetic potentials greater significance in quantum physics than in classical physics. Actually the original AB effect belongs to an ``electromagnetism-type". A certain type of vector potential is crucial for building the corresponding type of AB effect. In this work, we focus on the ``spin-type" AB effect. First, we derive the spin vector potential by considering a particle with a spin operator. Second, based on the spin vector potential we propose the spin AB effect, which is a gedanken double-slit interference experiment and is possible to observed in the lab. Third, we discuss the connections between the spin vector potential and some important spin interactions and predict a new type of spin-orbital interaction. Our result advances the study of the potential theory and opens a new avenue of the spin AB effect.