Three-site fermionic operator in systems of spinless fermions

[mykhailo_rakov]

Hello!

While working wth systems of spinless fermions, I ran into a problem with construction of the Hamiltonian terms which are three-site. They look like $\psi^{\dagger} U^{\dagger} \psi$. $U$-operator represents local gauge field and has mathematically the same form as $\psi$-operator.

I create a class as follows:
class FermionChain2(CouplingMPOModel)

and put in the appropriate commands. In my case the unit cell has 4 sites ($\psi$-operators sit on odd sites and $U$-operators sit on even sites).
The command for three-site term is
self.add_multi_coupling(-w, [('Cd',[0],0),('Cd',[0],1),('C',[0],2)], plus_hc=True)

During execution, Python marks this command in yellow, and yields the following error:
Value error: Invalid coupling: odd number of operators which need 'JW' string

Does anyone know how to properly construct such term?
Thank everyone in advance.

Just in case, I mention here some of the modules which I import from Tenpy:
from tenpy.models.model import CouplingModel, NearestNeighborModel, MPOModel, CouplingMPOModel
from tenpy.models.fermions_spinless import FermionModel
from tenpy.networks.site import FermionSite

[Johannes]

The error comes because you try to add a term with 3 fermionic operators - this would require an open Jordan wigner string when mapping to spins, and thus be a non-local operator. More generally, you can't write physical Hamiltonians with an odd number of fermionic operators, because they violate locality.

I guess you actually want a bosonic/spin site for the U operators?