Time evolution of Hamiltonian containing 4-operator term with MPO.

Question

Hi,
I am trying to time evolution of a wave-packet using MPO time evolution, with multi-Hubbard Hamiltonian, which has four operator terms.
ampo +=Jh,"Cdagdn",b,"Cdagup",b,"Cup",b+1,"Cdn",b+1;
ampo +=Jh,"Cdagdn",b+1,"Cdagup",b+1,"Cup",b,"Cdn",b;
Where, I found the problem with "auto expH = toExpH(ampo,tau*Cplx_i);;"
while running it's give error:

From line 1490, file mps/autompo.cc

Only at most 2-operator terms allowed for AutoMPO conversion to MPO/IQMPO

Only at most 2-operator terms allowed for AutoMPO conversion to MPO/IQMPO
Aborted (core dumped)

Please help me to solve this issue.

Answer 1

Hi, so unfortunately our toExpH feature is limited to Hamiltonians consisting of at most 2-operator terms only. The reason is that it's technical to extend the same method that lets AutoMPO work for > 2 operator terms to also define the exponential of H, even though in principle this could be done perhaps.

But additionally, since implementing toExpH, we and the tensor network community have found that MPO-based time evolution is not a particulary reliable or accurate time-evolution method (in relative terms, since it does work but just not as well) compared to other methods. The best method to use would be TDVP which only needs the Hamiltonian MPO as input. (See the recent review by Paeckel et al. for a technical discussion of both time-evolution methods.) So this is unfortunate given the convenience of MPO methods, but is a useful thing to keep in mind.

Best regards,
Miles