## Three-site fermionic operator in systems of spinless fermions

How do I use this algorithm? What does that parameter do?
mykhailo_rakov
Posts: 1
Joined: 23 Jan 2024, 04:37

### Three-site fermionic operator in systems of spinless fermions

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

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?

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
Posts: 442
Joined: 21 Jul 2018, 12:52
Location: TU Munich

### Re: Three-site fermionic operator in systems of spinless fermions

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?