  We examine the time evolution of an asymmetric Hubbard dimer, which has a
different on-site interaction on the two sites. The Hamiltonian has a
time-dependent hopping term, which can be employed to describe an electric
field (which creates a Hamiltonian with complex matrix elements), or it can
describe a modulation of the lattice (which has real matrix elements). By
examining the symmetries under spin and pseudospin, we show that the former
case involves at most a 3 x 3 block---it can be mapped onto the time evolution
of a time-independent Hamiltonian, so the dynamics can be evaluated
analytically and exactly (by solving a nontrivial cubic equation). We also show
that the latter case reduces to at most 2 x 2 blocks, and hence the time
evolution for a single Trotter step can be determined exactly, but the time
evolution generically requires a Trotter product.
