I am trying to reproduce the result, especially the charge pumping result of arXiv:1407.6985. I directly use the module tenpy.models.haldane.FermionicHaldaneModel since it's just the Hamiltonian eq(1) in arXiv:1407.6985. To be concrete, let me show you the Hamiltonian:

\(H = -t_1\sum_{<ij>}c_i^\dagger c_j-t_2\sum_{<<ij>>}e^{i\phi_{ij}}c_i^\dagger c_j+m\sum_u (n_{u,A}-n_{u, B})+V\sum_{u}n_{u, A}n_{u, B}\)

The geometry is an infinite cylinder with circumference \(L_y\) which is the number of unit cells in the y direction(the finite periodic direction). The unit cell of the uMPS includes \(L_y\) lattice unit cells in a leg(\(2L_y\) sites). I have chosen two parameter dictionaries to reproduce Fig.2. of arXiv:1407.6985. They are:

Code: Select all

```
# Parameter for \nu=1 Chern Insulator
param_CI = { "bc_MPS": "infinite",
"bc_x": "periodic",
"bc_y": "cylinder",
"conserve": "N",
"Lx": 1,
"Ly": 3,
"order": "default",
"mu": 0.,
"V": 0.0,
"t1": -1., # leave t2 to be the default value
"phi_ext": phi_ext
}
# Parameter for \nu=1/3 Fractional Chern Insulator
param_FCI = { "bc_MPS": "infinite",
"bc_x": "periodic",
"bc_y": "cylinder",
"conserve": "N",
"Lx": 1,
"Ly": 6,
"order": "default",
"mu": 0.,
"V": 1.0,
"t1": -1., # leave t2 to be the default value
"phi_ext": phi_ext
}
```

Since in both cases(CI and FCI) the systems are gapped, I think there is no gaplessness problem. I have tried to increase the interaction \(V\) in the FCI case to avoid competing with the metal phase but it doesn't work.

So, I want some suggestions from people who are familiar with iDMRG implementation or FCI systems.

Sincerely,

Xiaohan Yang