def test_default():
p = Parameters({'a': 1, 'b': "foo"})
assert p.get('c', "default") == "default"
with pytest.raises(KeyError):
p.get('c')
def test_tightbinding_honeycomb():
nearestNeighbors = {
RegularChain: 2,
SquareLattice: 4,
HoneycombLattice: 3,
KagomeLattice: 4,
RubyLattice: 4,
LiebLattice: 2 * np.sqrt(2)
}
for latticeT, nn in nearestNeighbors.items():
lattice = latticeT()
params = Parameters({'lattice': lattice, 't': 1})
s = TightBindingSystem(params)
path = lattice.getKvectorsPath(resolution=3, pointlabels=['G', 'X'])
bandstructure = s.solve(path)
assert len(path.points) == 4
# Energy at the Gamma point
g = bandstructure.energies[1][0]
print("Lattice type: {}".format(latticeT))
np.testing.assert_almost_equal(g, -params['t'] * nn)
def test_chern_number_dipolar_honeyomb():
lattice = HoneycombLattice()
params = Parameters({
'lattice': lattice,
'cutoff': 3,
'tbar': 1,
't': 0.54,
'w': 3,
'mu': 2.5
})
s = DipolarSystem(params)
bbox = lattice.getKvectorsRhomboid(50)
bandstructure = s.solve(bbox)
chernNumbers = [
bandstructure.getBerryFlux(n) / (2 * np.pi) for n in range(4)
]
np.testing.assert_almost_equal(chernNumbers, [1, 0, -3, 2], decimal=1)
chernNumbers = [
bandstructure.getBerryFlux(n, alternative_algorithm=True) / (2 * np.pi)
for n in range(4)
]
np.testing.assert_almost_equal(chernNumbers, [1, 0, -3, 2], decimal=1)
def test_paramter_change(recwarn):
lattice = RegularChain()
params = Parameters({'lattice': lattice, 't': 1})
s = TightBindingSystem(params)
path = lattice.getKvectorsPath(resolution=2, pointlabels=['G', 'X'])
# Solve for t = 1
bs = s.solve(path)
en = bs.energies
# Change the parameter of the model
s.params["t"] = 2
# This is supposed to print a warning
# because we did not call initialize()
bs = s.solve(path)
assert issubclass(recwarn.pop().category, UserWarning)
# Solve again
s.initialize()
bs = s.solve(path)
en2 = bs.energies
# All energies should be twice as high
assert np.all(2 * en == en2)
def test_simple():
p = Parameters({'a': 1, 'b': "foo"})
assert p['a'] == 1
assert p['b'] == "foo"
p['a'] = "bar"
assert p['a'] == "bar"
def test_chern_number_dipolar_honeyomb():
lattice = HoneycombLattice()
params = Parameters({
'lattice': lattice,
'cutoff': 3,
'tbar': 1,
't': 0.54,
'w': 3,
'mu': 2.5
})
s = DipolarSystem(params)
bzone = lattice.getKvectorsZone(50)
bandstructure = s.solve(bzone)
chernNumbers = bandstructure.getBerryFlux() / (2 * np.pi)
np.testing.assert_almost_equal(chernNumbers, [1, 0, -3, 2], decimal=1)
def test_tightbinding_honeycomb():
lattice = HoneycombLattice()
params = Parameters({
'lattice': lattice,
't': 1
})
s = TightBindingSystem(params)
path = lattice.getKvectorsPath(resolution=4, pointlabels=['A', 'G', 'X'])
assert len(path.points) == 6
bandstructure = s.solve(path)
np.testing.assert_almost_equal(bandstructure.energies[0][0], -1)
np.testing.assert_almost_equal(bandstructure.energies[1][0], 0)
np.testing.assert_almost_equal(bandstructure.energies[2][0], -2)
np.testing.assert_almost_equal(bandstructure.energies[3][0], -3)
np.testing.assert_almost_equal(bandstructure.energies[5][0], -1)
def test_dipolar_square():
lattice = SquareLattice()
params = Parameters({
'lattice': lattice,
'cutoff': 10.001,
'tbar': 1,
't': 0,
'w': 0
})
s = DipolarSystem(params)
path = lattice.getKvectorsPath(resolution=4, pointlabels=['A', 'G', 'X'])
bandstructure = s.solve(path)
# Energy at high symmetry points:
g = bandstructure.energies[3][0]
m = bandstructure.energies[1][0]
x = bandstructure.energies[5][0]
# The following values are calculated analytically (for cutoff=10.001) by Mathematica
np.testing.assert_almost_equal(g, -8.407854761)
np.testing.assert_almost_equal(m, +2.641343369)
np.testing.assert_almost_equal(x, +0.935057004)
s.params["tbar"] = 0
s.params["w"] = 1
s.initialize()
bandstructure = s.solve(path)
# Energy at high symmetry points:
g = bandstructure.energies[3][0]
m = bandstructure.energies[1][0]
x = bandstructure.energies[5][0]
np.testing.assert_almost_equal(g, 0.0)
np.testing.assert_almost_equal(m, 0.0)
np.testing.assert_almost_equal(x, -3.719360597)
res = v * np.all(dr.vectors == [-0.5, 0.2], axis=3) \
+ v * np.all(dr.vectors == [0.5, -0.2], axis=3) \
+ w * np.all(dr.vectors == [0.5, 0.2], axis=3) \
+ w * np.all(dr.vectors == [-0.5, -0.2], axis=3)
return np.array([1]) * res[:, :, :, None, None]
lattice = RegularChain()
lattice.addBasisvector([0.5, -0.2])
params = Parameters({
'lattice': lattice,
# tunneling strength NW, SE (inter-cell)
'v': -0.3,
# tunneling strength NE, SW (intra-cell)
'w': +.5
})
s = SSHModel(params)
# Infinite chain: calculate Berry phase
bs = s.solve(lattice.getKvectorsZone(300))
print(np.round(bs.getBerryPhase(), 2))
# Finite chain: spectrum and edge states
nSites = 40
lattice.makeFiniteAlongdirection(0, 40)
s.initialize()
#!/usr/bin/env python3
import sys
sys.path.append("../")
from bandstructure import Parameters
from bandstructure.system import TightBindingSystem
from bandstructure.lattice import HoneycombLattice
lattice = HoneycombLattice()
params = Parameters({'lattice': lattice, 't': 1})
s = TightBindingSystem(params)
# Solve system on high-symmetry path through Brillouin zone
path = lattice.getKvectorsPath(resolution=300,
pointlabels=['A', 'G', 'X', 'A'])
bandstructure = s.solve(path)
bandstructure.plot("dispersion.pdf")