TEBD for non-hermitian Hamiltonians

[jhauschild]

People start to think about non-hermitian Hamiltonians.
DMRG would need major adjustments for that, but TEBD could be adjusted quite simply.
Like in the imaginary time evolution with hermitian H, it would lead to non-hermitian U = expm(-i*dt *H_bond), but that's probably fine as long as the time step is small enough, and one could do the left-right-sweep instead of the brick-wall pattern to account for that.

Right now, the only point where it actually does break down is in generating the correct U=expm(-i*dt*H), because it does that by diagonalizing the H = V E V^dagger with eigh under the assumption that H is hermitian, and computing U = V exp(-i dt E) V^dagger.
For non-hermitian H, V V^dagger is no longer the identity, so one would need to compute matrix inverses in Engine._calc_U_bond. Alternatively, and probably better, one could overwrite that function Engine._calc_U_bond to not use the diagonalized H and instead use something like scipy.linalg.expm blockwise, which is already implemented for np_conserved Arrays in expm.