Issue with Missing Subscripts on Fermionic Operators in all_coupling_terms().to_TermList() Output

[Gun]

Hi everyone.

I am new to TeNPy and currently working on a project involving spin-half fermions. I’ve come across an issue with the output format from the all_coupling_terms().to_TermList() when using the add_coupling function for defining hopping terms.

Description of the Issue:

The output seems to correctly incorporate Jordan-Wigner strings and represents the intended couplings, but I noticed that the fermionic creation operator Cdd does not display subscripts in some cases where I would expect them. For example, I see Cdd JW_0 Cd_1 instead of the expected Cdd_0 JW_0 Cd_1 and similarly, Cdd JW_1 Cd_2 instead of Cdd_1 JW_1 Cd_2. Interestingly, the 'N' operators do have the correct subscripts.

This inconsistency has left me unsure whether this is just a cosmetic issue in the printout or if it suggests a deeper issue with how the model setup or the library handles fermionic terms (or my understanding of the output ). Could this lack of subscripts affect the accuracy or functionality of simulations run with this model?

Below I have provided example of a code.


Code:

Code: Select all

import numpy as np
from tenpy.models.lattice import Chain
from tenpy.models.model import CouplingMPOModel

class test(CouplingMPOModel):
    default_lattice = Chain
    force_default_lattice = True

    def init_sites(self, model_params):
        return site.SpinHalfFermionSite(cons_N=None,cons_Sz=None)
    def init_terms(self, model_params):
        J = 1.
        lambd=model_params.get('lambd',0) #get the lambda value from parameters
        self.add_coupling(lambd, 0, 'Cdd', 0, 'Cd', [1],plus_hc=True)
        self.add_coupling(1,0,'Nd',0,'Nd',[1],plus_hc=False)
test = test({'lambd':5,'L':3})
print(test.all_coupling_terms().to_TermList())

Output:

Code: Select all

5.00000 * Cdd JW_0 Cd_1 +
5.00000 * JW Cd_0 Cdd_1 +
1.00000 * Nd_0 Nd_1 +
5.00000 * Cdd JW_1 Cd_2 +
5.00000 * JW Cd_1 Cdd_2 +
1.00000 * Nd_1 Nd_2

[Gun]

Hi again,

I wanted to provide additional information. I have encountered a similar problem when using the add_multi_coupling function for defining four-point interactions.

More relevant to my project I am trying to implement intearctions of the form:

\(f^\dagger_{i\downarrow}f_{i\uparrow}f^\dagger_{i+1\uparrow}f_{i+1\downarrow}\)

The corresponding Python code snippet using add_multi_coupling is:

Code: Select all

        self.add_multi_coupling(1,[('Cdd',0,0),('Cu',0,0),('Cdu',1,0),('Cd',1,0)],plus_hc=False)

However, when I print the coupling terms for L=3L=3 in a chain geometry, the output I receive is:

Code: Select all

1.00000 * Cdd Cu_0 Cdu Cd_1 +
1.00000 * Cdd Cu_1 Cdu Cd_2 +
1.00000 * Cdd Cu_2 Cdu Cd_3 +
1.00000 * Cdd Cu_3 Cdu Cd_4

Thank you!

[Johannes]

The subscript notation is a bit misleading here, because it suggests that it only applies to the next operator.
Really, you should read those operators to be grouped like this:

Code: Select all

1.00000 * (Cdd Cu)_0 (Cdu Cd)_1 +
1.00000 * (Cdd Cu)_1 (Cdu Cd)_2 +
1.00000 * (Cdd Cu)_2 (Cdu Cd)_3 +
1.00000 * (Cdd Cu)_3 (Cdu Cd)_4

To understand that reasoning, you should know that the get_op method, which translates the strings of operator names to npc Arrays, takes whitespace concatenated operators as products of local operators multiplied together - as you would by hand when you write them.

[Johannes]

I've quickly fixed that formatting to include brackets in 9739ac3a4e26cbbfada009ec6bef6c3d7286a0a8

[Gun]

Thanks for the quick fix. Now I am sure I have the correct operators!