Time evolution of magnetic Bloch oscillations using TEBD

Abstract

Linear-chain ferromagnets such as \ce{CoCl_2\cdot 2H_2 O} have been shown to be capable of magnetic Bloch oscillations. This means that domain walls in he material undergo Bloch oscillations, resulting in an oscilling magnetization. It was recently suggested to use lasers in resonance with energies from the Wannier-Zeeman ladder to provoke such oscillations. Simulating this process in the fully interacting system requires quantum many-body simulations. Since the system is one-dimensional, the method of time-evolving block decimation (TEBD) seems appropriate. We describe and implement this method and use it to simulate lasers acting on the linear chain. This results in robust oscillations in the magnetization with the expected Bloch frequency, with little sign of decoherence.