  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.
