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Commit 0a9e7282 authored by Antonio Manesco's avatar Antonio Manesco
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update examples

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examples/1d_hubbard.ipynb 0 → 100644
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%% Cell type:code id:cb509096-42c6-4a45-8dc4-a8eed3116e67 tags:
``` python
import kwant
import numpy as np
import matplotlib.pyplot as plt
from codes import utils, hf, kwant_examples
from tqdm import tqdm
```
%% Cell type:code id:c22c6258-9ee8-4ccf-bfd8-94d50d27114d tags:
``` python
def hamiltonian(k):
tk = (1 + np.exp(1j * k)) * np.eye(2)
return np.block([
[0 * np.eye(2), tk],
[tk.conj(), 0 * np.eye(2)]
])
```
%% Cell type:code id:d31cbfea-18ea-454e-8a63-d706a85cd3fc tags:
``` python
# Compute non-interacting Hamiltonian on a coarse k-point grid
# Number of k-points along each direction
nk = 50
# k-points must start at zero
ks = np.linspace(0, 2 * np.pi, nk, endpoint=False)
hamiltonians_0 = np.array([hamiltonian(k) for k in ks])
hopping_vecs = np.array([[0,], [1,], [-1,]])
```
%% Cell type:code id:b39a2976-7c35-4670-83ef-12157bd3fc0e tags:
``` python
vals, vecs = np.linalg.eigh(hamiltonians_0)
plt.plot(ks, vals)
plt.show()
```
%% Output
%% Cell type:code id:41bd9f60-8f29-4e7c-a0c4-a0bbf66445b2 tags:
``` python
def compute_gap(
H_int,
ks,
ks_dense,
hamiltonians_0=hamiltonians_0,
filling=2,
tol=1e-5,
mixing=0.01,
order=10,
guess=None
):
# Generate guess on the same grid
if guess is None:
guess = utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=1)
else:
guess += np.max(guess) * utils.generate_guess(ks, hopping_vecs, ndof=hamiltonians_0.shape[-1], scale=0.1)
# Find groundstate Hamiltonian on the same grid
hk = hf.find_groundstate_ham(
H_int=H_int,
filling=filling,
hamiltonians_0=hamiltonians_0,
tol=tol,
guess=guess,
mixing=mixing,
order=order,
)
# Diagonalize groundstate Hamiltonian
vals, vecs = np.linalg.eigh(hk)
# Extract dense-grid Fermi energy
E_F = utils.get_fermi_energy(vals, filling)
gap = utils.calc_gap(vals, E_F)
return gap, hk - hamiltonians_0, vals - E_F
```
%% Cell type:code id:32b9e7c5-db12-44f9-930c-21e5494404b8 tags:
``` python
def compute_phase_diagram(
Us,
ks,
ks_dense,
tol=1e-5,
mixing=0.01,
order=10,
):
# onsite interactions
v_int = np.block(
[[np.ones((2, 2)), np.zeros((2, 2))], [np.zeros((2, 2)), np.ones((2, 2))]]
)
v_int = np.array([v_int for k in ks])
gap = []
vals = []
guess = None
for U in tqdm(Us):
H_int = U * v_int
_gap, guess, _vals = compute_gap(
H_int=H_int,
ks=ks,
ks_dense=ks_dense,
tol=tol,
mixing=mixing,
order=order,
guess=guess,
)
gap.append(_gap)
vals.append(_vals)
return np.asarray(gap, dtype=float), np.asarray(vals)
```
%% Cell type:code id:6a8c08a9-7e31-420b-b6b4-709abfb26793 tags:
``` python
# Generate dense-grid k-points
nk_dense = 100
ks_dense = np.linspace(0, 2 * np.pi, nk_dense, endpoint=True)
# Interaction strengths
Us = np.linspace(0, 3, 10, endpoint=True)
gap, vals = compute_phase_diagram(Us, ks=ks, ks_dense=ks_dense, tol=1e-9)
```
%% Output
100%|██████████| 10/10 [00:07<00:00, 1.34it/s]
%% Cell type:code id:e17fc96c-c463-4e1f-8250-c254d761b92a tags:
``` python
import xarray as xr
ds = xr.Dataset(
data_vars=dict(
vals=(["Us", "ks", "n"], vals),
gap=(["Us"], gap)
),
coords=dict(Us=Us, ks=ks, n=np.arange(vals.shape[-1])),
)
```
%% Cell type:code id:868cf368-45a0-465e-b042-6182ff8b6998 tags:
``` python
ds.vals.plot.scatter(x='ks', hue='Us')
plt.axhline(0)
```
%% Output
<matplotlib.lines.Line2D at 0x7f008b4ef350>
%% Cell type:code id:ac2eb725-f3bd-4d5b-a509-85d0d0071958 tags:
``` python
ds.gap.plot()
```
%% Output
[<matplotlib.lines.Line2D at 0x7f007257b690>]
%% Cell type:code id:0cb395cd-84d1-49b4-89dd-da7a2d09c8d0 tags:
``` python
ds.to_netcdf('./data/1d_hubbard_example.nc')
```
examples/data/1d_hubbard_example.nc 0 → 100644
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− 0
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File added
examples/graphene_extended_hubbard.ipynb
+ 76
− 173
View file @ 0a9e7282
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