Magnetic Bloch oscillations in a non-Hermitian quantum Ising chain

We investigate the impacts of an imaginary transverse field on the dynamics of magnetic domain walls in a quantum Ising chain. We show that an imaginary field plays a similar role as a real transverse field in forming a low-lying Wannier-Stark ladder. However, analytical and numerical calculations of the time evolutions in both systems show that the corresponding Bloch oscillations exhibit totally different patterns for the same initial states. These findings reveal the nontrivial effect of non-Hermiticity on quantum spin dynamics.