def test_join_incompatible_dimension():
"""Test that models with unequal dimension can not be joined."""
model1 = tbmodels.Model(hop={(0, ): np.eye(3)})
model2 = tbmodels.Model(hop={(0, 0): np.eye(3)})
with pytest.raises(ValueError) as excinfo:
tbmodels.Model.join_models(model1, model2)
assert "dimension" in str(excinfo.value)
def test_join_incompatible_unit_cell():
"""Test that models with unequal unit cell can not be joined."""
model1 = tbmodels.Model(uc=np.eye(3), size=2)
model2 = tbmodels.Model(uc=np.eye(3), size=2)
model3 = tbmodels.Model(uc=np.diag([1.1, 1, 1]), size=2)
with pytest.raises(ValueError) as excinfo:
tbmodels.Model.join_models(model1, model2, model3)
assert "unit cell" in str(excinfo.value)
def test_non_hermitian_1():
"""
Check that an error is raised when the given hoppings do not correspond
to a hermitian Hamiltonian.
"""
with pytest.raises(ValueError):
tbmodels.Model(size=2, hop={(0, 0, 0): np.eye(2), (1, 0, 0): np.eye(2)})
def test_invalid_hopping_matrix():
"""
Check that an error is raised when the passed size does not match the
shape of hopping matrices.
"""
with pytest.raises(ValueError):
tbmodels.Model(size=2, hop={(0, 0, 0): np.eye(4)})
def test_unequal_orbital_number():
model = tbmodels.Model(pos=[[0., 0.], [0.5, 0.5], [0.5, 0.5]],
on_site=[1, 0.7, -1.2])
t1 = 0.1
t2 = 0.15
t3 = 0.4
for phase, R in zip([1, -1j, 1j, -1], itertools.product([0, -1], [0, -1])):
model.add_hop(t1 * phase, 0, 1, R)
model.add_hop(t3 * phase, 1, 2, R)
for R in ((r[0], r[1]) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(-t2, 1, 1, R)
model.add_hop(-t2, 2, 2, R)
latt = model.to_kwant_lattice()
sym = kwant.TranslationalSymmetry(latt.vec((1, 0)), latt.vec((0, 1)))
sys = kwant.Builder(sym)
sys[latt.shape(lambda p: True, (0, 0))] = 0
model.add_hoppings_kwant(sys)
sys = wraparound.wraparound(sys).finalized()
for k in KPT:
k = k[:2]
k_kwant = tuple(np.array(k) * 2 * np.pi)
np.testing.assert_allclose(model.eigenval(k),
la.eigvalsh(
sys.hamiltonian_submatrix(k_kwant)),
atol=1e-8)
def tb_model():
"""
Creates a simple TBmodels tight-binding model.
"""
t1, t2 = (0.2, 0.3)
model = tbmodels.Model(on_site=(1, 1, -1, -1),
pos=[[0., 0., 0.], [0., 0., 0.], [0.5, 0.5, 0.],
[0.5, 0.5, 0.]],
occ=2)
for p, R in zip([1, 1j, -1j, -1], itertools.product([0, -1], [0, -1],
[0])):
model.add_hop(overlap=p * t1, orbital_1=0, orbital_2=2, R=R)
model.add_hop(overlap=p.conjugate() * t1,
orbital_1=1,
orbital_2=3,
R=R)
for R in ((r[0], r[1], 0) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(t2, 1, 1, R)
model.add_hop(-t2, 2, 2, R)
model.add_hop(-t2, 3, 3, R)
return model
def HaldaneTB(delta,t1,hop2,phi):
# define lattice vectors
lat=[[1.0,0.0],[0.5,np.sqrt(3.0)/2.0]]
# define coordinates of orbitals
orb=[[1./3.,1./3.],[2./3.,2./3.]]
# make two dimensional tight-binding Haldane model
haldane=tbm.Model(on_site=[-delta,delta],
dim=2,
pos=orb,
uc=np.array(lat))
# set model parameters
t2=hop2*np.exp(1.j*phi)
# set hoppings (one for each connected pair of orbitals)
# from j in R to i in 0
# (amplitude, i, j, [lattice vector to cell containing j])
haldane.add_hop(t1, 0, 1, [ 0, 0])
haldane.add_hop(t1, 1, 0, [ 1, 0])
haldane.add_hop(t1, 1, 0, [ 0, 1])
# add second neighbour complex hoppings
haldane.add_hop(t2 , 0, 0, [ 0, -1])
haldane.add_hop(t2 , 0, 0, [ 1, 0])
haldane.add_hop(t2 , 0, 0, [ -1, 1])
haldane.add_hop(t2 , 1, 1, [ -1, 0])
haldane.add_hop(t2 , 1, 1, [ 1,-1])
haldane.add_hop(t2 , 1, 1, [ 0, 1])
return haldane
def test_non_hermitian_1():
with pytest.raises(ValueError):
model = tbmodels.Model(size=2,
hop={
(0, 0, 0): np.eye(2),
(1, 0, 0): np.eye(2)
})
def inner(t1, t2, sparsity_default=False, **kwargs):
dim = kwargs.get("dim", 3)
defaults = {}
defaults["pos"] = [[0] * 2, [0.5] * 2]
if dim < 2:
raise ValueError("dimension must be at least 2")
if dim > 2:
for position in defaults["pos"]:
position.extend([0] * (dim - 2))
defaults["occ"] = 1
defaults["on_site"] = (1, -1)
defaults["size"] = 2
defaults["dim"] = None
defaults["sparse"] = sparsity_default
model = tbmodels.Model(**ChainMap(kwargs, defaults))
for phase, r_part in zip([1, -1j, 1j, -1],
itertools.product([0, -1], [0, -1])):
R = list(r_part)
R.extend([0] * (dim - 2))
model.add_hop(t1 * phase, 0, 1, R)
for r_part in itertools.permutations([0, 1]):
R = list(r_part)
R.extend([0] * (dim - 2))
model.add_hop(t2, 0, 0, R)
model.add_hop(-t2, 1, 1, R)
return model
def test_unequal_orbital_number():
"""
Check converting a simple model to kwant, where the two positions
don't have an equal number of orbitals.
"""
model = tbmodels.Model(pos=[[0., 0.], [0.5, 0.5], [0.5, 0.5]], on_site=[1, 0.7, -1.2])
t1 = 0.1
t2 = 0.15
t3 = 0.4
for phase, R in zip([1, -1j, 1j, -1], itertools.product([0, -1], [0, -1])):
model.add_hop(t1 * phase, 0, 1, R)
model.add_hop(t3 * phase, 1, 2, R)
for R in ((r[0], r[1]) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(-t2, 1, 1, R)
model.add_hop(-t2, 2, 2, R)
latt = model.to_kwant_lattice()
sym = kwant.TranslationalSymmetry(latt.vec((1, 0)), latt.vec((0, 1))) # pylint: disable=no-member
sys = kwant.Builder(sym) # pylint: disable=no-member
sys[latt.shape(lambda p: True, (0, 0))] = 0
model.add_hoppings_kwant(sys)
sys = wraparound.wraparound(sys).finalized()
for k in KPT:
k = k[:2]
np.testing.assert_allclose(
model.eigenval(k), la.eigvalsh(sys.hamiltonian_submatrix(params=to_kwant_params(k))), atol=1e-8
)
def test_invalid_empty():
"""
Check that trying to convert an incomplete tight-binding model to
hr format raises an error.
"""
model = tbmodels.Model(size=2, dim=3)
with pytest.raises(ValueError):
model.to_hr()
def test_wrong_key_length():
with pytest.raises(ValueError):
model = tbmodels.Model(size=2,
hop={
(0, 0, 0): np.eye(2),
(1, 0, 0): np.eye(2),
(-1, 0, 0, 0): np.eye(2)
},
contains_cc=False)
def test_wrong_pos_dim():
with pytest.raises(ValueError):
model = tbmodels.Model(size=2,
hop={
(0, 0, 0): np.eye(2),
(1, 0, 0): np.eye(2),
(-1, 0, 0): np.eye(2)
},
contains_cc=False,
pos=((0., ) * 3, (0.5, ) * 4))
def test_wrong_uc_shape():
with pytest.raises(ValueError):
model = tbmodels.Model(size=2,
hop={
(0, 0, 0): np.eye(2),
(1, 0, 0): np.eye(2),
(-1, 0, 0): np.eye(2)
},
contains_cc=False,
pos=((0., ) * 3, (0.5, ) * 3),
uc=np.array([[1, 2], [3, 4], [5, 6]]))
def test_wrong_key_length():
"""
Check that an error is raised when the reciprocal lattice vectors
have inconsistent lengths.
"""
with pytest.raises(ValueError):
tbmodels.Model(
size=2,
hop={(0, 0, 0): np.eye(2), (1, 0, 0): np.eye(2), (-1, 0, 0, 0): np.eye(2)},
contains_cc=False,
)
def test_compare_pythtb():
pt_model = pt.tb_model(1, 1, lat=[[1]], orb=[[0], [0.2]])
tb_model = tb.Model(dim=1, pos=[[0], [0.2]], uc=[[1]])
pt_model.set_hop(3j, 0, 1, [1])
tb_model.add_hop(3j, 0, 1, [1])
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0])).all()
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0], convention=1)).all()
assert np.isclose(pt_model._gen_ham([1]), tb_model.hamilton([1], convention=1)).all()
assert np.isclose(pt_model._gen_ham([0.2]), tb_model.hamilton(0.2, convention=1)).all()
def test_wrong_uc_shape():
"""
Check that an error is raised when the unit cell is not square.
"""
with pytest.raises(ValueError):
tbmodels.Model(
size=2,
hop={(0, 0, 0): np.eye(2), (1, 0, 0): np.eye(2), (-1, 0, 0): np.eye(2)},
contains_cc=False,
pos=((0.0,) * 3, (0.5,) * 3),
uc=np.array([[1, 2], [3, 4], [5, 6]]),
)
def test_wrong_pos_dim():
"""
Check that an error is raised when the positions have inconsistent
dimensions.
"""
with pytest.raises(ValueError):
tbmodels.Model(
size=2,
hop={(0, 0, 0): np.eye(2), (1, 0, 0): np.eye(2), (-1, 0, 0): np.eye(2)},
contains_cc=False,
pos=((0.0,) * 3, (0.5,) * 4),
)
def test_wrong_pos_length():
"""
Check that an error is raised when the number of positions does not
match the given size.
"""
with pytest.raises(ValueError):
tbmodels.Model(
size=2,
hop={(0, 0, 0): np.eye(2), (1, 0, 0): np.eye(2), (-1, 0, 0): np.eye(2)},
contains_cc=False,
pos=((0.0,) * 3, (0.5,) * 3, (0.2,) * 3),
)
def test_compare_pythtb():
"""
Compare a tight-binding model against a PythTB reference, using convention 1.
"""
pt_model = pt.tb_model(1, 1, lat=[[1]], orb=[[0], [0.2]])
tb_model = tb.Model(dim=1, pos=[[0], [0.2]], uc=[[1]])
pt_model.set_hop(3j, 0, 1, [1])
tb_model.add_hop(3j, 0, 1, [1])
# pylint: disable=protected-access
assert np.isclose(pt_model._gen_ham([0]), tb_model.hamilton([0])).all()
assert np.isclose(pt_model._gen_ham([0]),
tb_model.hamilton([0], convention=1)).all()
assert np.isclose(pt_model._gen_ham([1]),
tb_model.hamilton([1], convention=1)).all()
assert np.isclose(pt_model._gen_ham([0.2]),
tb_model.hamilton(0.2, convention=1)).all()
def tbmodels_Haldane():
delta=0.2
t=-1.0
t2 =0.15*np.exp((1.j)*np.pi/2.)
t2c=t2.conjugate()
my_model = tbmodels.Model(
on_site=[delta, -delta],uc = [[1.0,0.0],[0.5,np.sqrt(3.0)/2.0]], dim=2, occ=1, pos=[[1./3.,1./3.],[2./3.,2./3.]]
)
my_model.add_hop(t, 0, 1, [ 0, 0])
my_model.add_hop(t, 1, 0, [ 1, 0])
my_model.add_hop(t, 1, 0, [ 0, 1])
my_model.add_hop(t2 , 0, 0, [ 1, 0])
my_model.add_hop(t2 , 1, 1, [ 1,-1])
my_model.add_hop(t2 , 1, 1, [ 0, 1])
my_model.add_hop(t2c, 1, 1, [ 1, 0])
my_model.add_hop(t2c, 0, 0, [ 1,-1])
my_model.add_hop(t2c, 0, 0, [ 0, 1])
return my_model
def tb_system():
t1, t2 = (0.2, 0.3)
model = tbmodels.Model(on_site=(1, 1, -1, -1),
pos=[[0., 0., 0.], [0., 0., 0.], [0.5, 0.5, 0.],
[0.5, 0.5, 0.]],
occ=2)
for p, R in zip([1, 1j, -1j, -1], itertools.product([0, -1], [0, -1],
[0])):
model.add_hop(overlap=p * t1, orbital_1=0, orbital_2=2, R=R)
model.add_hop(overlap=p.conjugate() * t1,
orbital_1=1,
orbital_2=3,
R=R)
for R in ((r[0], r[1], 0) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(t2, 1, 1, R)
model.add_hop(-t2, 2, 2, R)
model.add_hop(-t2, 3, 3, R)
return z2pack.tb.System(model)
def inner(t1, t2, sparsity_default=False, **kwargs):
dim = kwargs.get('dim', 3)
defaults = {}
defaults['pos'] = [[0] * 2, [0.5] * 2]
if dim < 2:
raise ValueError('dimension must be at least 2')
elif dim > 2:
for p in defaults['pos']:
p.extend([0] * (dim - 2))
defaults['occ'] = 1
defaults['on_site'] = (1, -1)
defaults['size'] = 2
defaults['dim'] = None
defaults['sparse'] = sparsity_default
model = tbmodels.Model(**ChainMap(kwargs, defaults))
for phase, R in zip([1, -1j, 1j, -1], itertools.product([0, -1], [0, -1], [0])):
model.add_hop(t1 * phase, 0, 1, R)
for R in ((r[0], r[1], 0) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(-t2, 1, 1, R)
return model
def test_invalid_hopping_matrix():
with pytest.raises(ValueError):
model = tbmodels.Model(size=2, hop={(0, 0, 0): np.eye(4)})
# Example for the interface TBmodels-WannierBerri. Extracted from
# http://www.physics.rutgers.edu/~dhv/pythtb-book-examples/ptb_samples.html
# but written in TBmodels format (http://z2pack.ethz.ch/tbmodels/doc/1.3/index.html)
# 3D model of Li on bcc lattice, with s orbitals only
# set tbmodel parameters
Es= 4.5 # site energy
t =-1.4 # hopping parameter
r0=np.array([-0.5, 0.5, 0.5])
r1=np.array([ 0.5,-0.5, 0.5])
r2=np.array([ 0.5, 0.5,-0.5])
uc=np.array([r0,r1,r2])# in rows
cc=True
tbmodel = tb.Model(on_site=[Es], dim=3, occ=1, pos=[[0.0,0.0,0.0]],uc=uc,contains_cc=cc)
# set hoppings along four unique bonds
# note that neighboring cell must be specified in lattice coordinates
for R in ([1,0,0],[0,1,0],[0,0,1],[1,1,1]):
tbmodel.add_hop(t, 0, 0, R)
system=wb.System_TBmodels(tbmodel,berry=True)
Efermi=np.linspace(-7,16,1000)
# Define the generators of the point group of the crystal (Im-3m)
# generators extracted from Bilbao Crystallographic Center
# (using same notation as https://www.cryst.ehu.es/cgi-bin/cryst/programs/nph-point_genpos?w2do=gens&num=32&what=)
# C2z axis (predefined): ITA200z=SYM.Rotation(2,[0,0,1])
# C2y axis (predefined): ITA20y0=SYM.Rotation(2,[0,1,0])
# Inversion (predefined)
ITA3M111=SYM.Rotation(3,[1,1,1])# C3 axis along 111
def test_size_from_hop():
"""
Check that the size can be obtained from hopping matrices.
"""
model = tbmodels.Model(hop={(0, 0, 0): np.zeros((4, 4))})
assert model.size == 4
def test_dim_from_uc():
"""Check that the dimension can be inferred from the unit cell."""
model = tbmodels.Model(uc=((1, 0), (0, 1)), size=5)
assert model.dim == 2
def test_invalid_empty():
model = tbmodels.Model(size=2, dim=3)
with pytest.raises(ValueError):
model.to_hr()
t1, t2 = (0.2, 0.3)
settings = {'num_lines': 11,
'pos_tol': 1e-2,
'gap_tol': 2e-2,
'move_tol': 0.3,
'iterator': range(8, 27, 2),
'min_neighbour_dist': 1e-2,
}
model = tbmodels.Model(
on_site=(1, 1, -1, -1),
pos=[
[0., 0., 0.],
[0., 0., 0.],
[0.5, 0.5, 0.],
[0.5, 0.5, 0.]
],
occ=2
)
for p, R in zip([1, 1j, -1j, -1], itertools.product([0, -1], [0, -1], [0])):
model.add_hop(overlap=p * t1, orbital_1=0, orbital_2=2, R=R)
model.add_hop(overlap=p.conjugate() * t1, orbital_1=1, orbital_2=3, R=R)
for R in ((r[0], r[1], 0) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(t2, 1, 1, R)
model.add_hop(-t2, 2, 2, R)
model.add_hop(-t2, 3, 3, R)
import tbmodels
import itertools
model = tbmodels.Model(
on_site=[1, -1],
dim=3,
occ=1,
pos=[[0., 0., 0.], [0.5, 0.5, 0.]]
)
t1, t2 = (0.1, 0.2)
for phase, R in zip([1, -1j, 1j, -1], itertools.product([0, -1], [0, -1], [0])):
model.add_hop(t1 * phase, 0, 1, R)
for R in ((r[0], r[1], 0) for r in itertools.permutations([0, 1])):
model.add_hop(t2, 0, 0, R)
model.add_hop(-t2, 1, 1, R)
