Can I perform a time evolution with TEBD for a non-Hermitian Hamiltonian?

[talentkeychen]

What is your issue?

Hi! Not sure if this feature is already available, but I want to perform a time evolution of an Hamiltonian $H=H_H+H_{nH}$ which is consist of two parts: the Hermitian part $H_{H}$ and the non-Hermitian part $H_{nH}$. The non-Hermitian Hamiltonian is actually a two-body dissipation one as $i \sum_{j=1}^{N-1} \sigma_z^j \sigma_z^j$. I wonder if there is a built-in feature in $\texttt{quimb}$? I understand that for the built-in $\texttt{tebd}$, we can perform the imaginary time evolution but what about this one?

[jcmgray]

Hi @talentkeychen, yes I think this should work just as-is, supplying the non-hermitian terms. The local evolution in the TEBD class is generated now as np.linalg.expm(real_or_imag_dt * hij), where hij could be any matrix.

I guess there might be some things to think about such as loss of norm, but I would just see what happens first - I haven't tested this kind of system myself.