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**