## Bosonic Haldane Model

How do I use this algorithm? What does that parameter do?
nervxxx
Posts: 5
Joined: 20 Aug 2020, 04:16

### Bosonic Haldane Model

I am going through some example models, and was looking at the Bosonic Haldane Model in particular:

https://github.com/tenpy/tenpy/blob/mas ... py#L13-L80

It is stated that the Hamiltonian reads
.. math ::
H = \sum_{ij} t_{ij} b_i^\dagger b_j + \sum_i \mu (n_{A, i} - n_{B, i})
+ V \sum_{\langle ij \rangle, i<j} n_{A, i} n_{B, j}
However, looking at the implementation of on-site terms I see

Code: Select all

        for u in range(len(self.lat.unit_cell)):
self.add_onsite(-mu, 1, 'N', category='mu N')
Is this code double-summing? I mean, the for-loop runs over u=0,1 of the honeycomb, and seems to repeat the same action in each pass. So it feels like it is implementing \sum_i 2\mu (n_{A,i} - n_{B,i}). Or, am I mistaken and not understanding its action correctly at all?
Johannes
Posts: 209
Joined: 21 Jul 2018, 12:52
Location: UC Berkeley

### Re: Bosonic Haldane Model

You're right, that's a double counting. Good catch, thanks for pointing it out!
The Fermionic Hofstadter model has the same problem, of course.