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Commit d7e96d28 authored by Antonio Manesco's avatar Antonio Manesco
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cleanup notebook

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1 merge request!3create solvers and interface modules
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%% Cell type:code id: tags:
``` python
import numpy as np
import matplotlib.pyplot as plt
from codes import utils, model, interface, solvers, hf
```
%% Cell type:code id: tags:
``` python
U0 = 1
nk = 1001
filling = 2
hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))
tb_model = {(0,): hopp + hopp.T.conj(), (1,): hopp, (-1,): hopp.T.conj()}
def model_U(U):
int_model = {
(0,): U * np.kron(np.eye(2), np.ones((2, 2))),
}
return model.Model(tb_model=tb_model, int_model=int_model)
model0 = model_U(U0)
model0.vectors = [*model0.int_model.keys()]
model0.random_guess(model0.vectors)
model0.kgrid_evaluation(nk=100)
```
%% Cell type:code id: tags:
``` python
hamiltonians_0 = utils.kgrid_hamiltonian(
nk=nk, hk=utils.model2hk(tb_model=tb_model), dim=1
)
def groundstate(U):
_model=model_U(U)
tb_mf_k = interface.find_groundstate_ham(
_model,
filling=filling,
nk=nk,
solver=solvers.rspace_solver,
cost_function=solvers.real_space_cost,
return_kspace=True,
optimizer_kwargs={},
)
vals, vecs = np.linalg.eigh(tb_mf_k)
EF = utils.get_fermi_energy(vals, filling)
densityMatrix = hf.density_matrix(vals, vecs, EF)
return tb_mf_k, densityMatrix, _model.H_int
tb_mf0, densityMatrix0, H_int0 = groundstate(U0)
mf0 = tb_mf0 - hamiltonians_0
@np.vectorize
def mfRescaled(alpha, mf0=mf0, H_int0=H_int0):
hamiltonian = hamiltonians_0 + mf0 * alpha
vals, vecs = np.linalg.eigh(hamiltonian)
EF = utils.get_fermi_energy(vals, filling)
densityMatrix = hf.density_matrix(vals, vecs, EF)
return hf.total_energy(
hamiltonians_0 + np.sign(alpha) * mf0,
densityMatrix,
)
```
%% Cell type:code id: tags:
``` python
alphas = np.linspace(-5, 5, 201)
plt.plot(alphas, mfRescaled(alphas), 'o')
plt.plot(-alphas, mfRescaled(alphas), 'o')
plt.axvline(x=1, c="k", ls="--")
plt.axvline(x=-1, c="k", ls="--")
plt.ylabel("Total Energy")
plt.xlabel(r"$\alpha$")
# plt.ylim(-4.6, -4.5)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
alphas = np.linspace(-5, 5, 201)
plt.plot(alphas, mfRescaled(alphas), 'o')
plt.plot(-alphas, mfRescaled(alphas), 'o')
plt.axvline(x=1, c="k", ls="--")
plt.axvline(x=-1, c="k", ls="--")
plt.ylabel("Total Energy")
plt.xlabel(r"$\alpha$")
# plt.ylim(-4.6, -4.5)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
alphas = np.linspace(-5, 5, 201)
plt.plot(alphas, mfRescaled(alphas), 'o')
plt.plot(-alphas, mfRescaled(alphas), 'o')
plt.axvline(x=1, c="k", ls="--")
plt.axvline(x=-1, c="k", ls="--")
plt.ylabel("Total Energy")
plt.xlabel(r"$\alpha$")
# plt.ylim(-4.6, -4.5)
plt.show()
```
%% Output
%% Cell type:code id: tags:
``` python
plt.plot(alphas[:-1], np.diff(mfRescaled(alphas)))
# plt.plot(-alphas[:-1], -np.diff(mfRescaled(alphas)))
plt.axhline(0, ls='--', c='k')
plt.axvline(x=1, c="k", ls="--")
plt.axvline(x=-1, c="k", ls="--")
# plt.ylim(-4, -2)
plt.show()
```
%% Output
......
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