def test_singular_fully_degenerate():
"""This testcase features a rectangular (and hence singular)
hopping matrix with complete degeneracy.
This case can still be treated with the Schur technique."""
w = 5 # width
t = 1.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = h_hop_s
h_cell = np.zeros((4*w, 4*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, 2*w:3*w] = h_hop_s
h_cell[w:2*w, w:2*w] = h_cell_s
h_cell[w:2*w, 3*w:4*w] = h_hop_s
h_cell[2*w:3*w, :w] = h_hop_s
h_cell[2*w:3*w, 2*w:3*w] = h_cell_s
h_cell[3*w:4*w, w:2*w] = h_hop_s
h_cell[3*w:4*w, 3*w:4*w] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_singular_degenerate_with_crossing():
"""This testcase features a rectangular (and hence singular)
hopping matrix with degeneracy k-values including a crossing
with velocities of opposite sign.
This case must be treated with the fall-back technique."""
w = 5 # width
t = 20.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = -h_hop_s
h_cell = np.zeros((4*w, 4*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, 2*w:3*w] = h_hop_s
h_cell[w:2*w, w:2*w] = -h_cell_s
h_cell[w:2*w, 3*w:4*w] = -h_hop_s
h_cell[2*w:3*w, :w] = h_hop_s
h_cell[2*w:3*w, 2*w:3*w] = h_cell_s
h_cell[3*w:4*w, w:2*w] = -h_hop_s
h_cell[3*w:4*w, 3*w:4*w] = -h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = -np.conj(leads.square_selfenergy(w, t, e))
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_singular_degenerate_with_crossing():
"""This testcase features a rectangular (and hence singular)
hopping matrix with degeneracy k-values including a crossing
with velocities of opposite sign.
This case must be treated with the fall-back technique."""
w = 5 # width
t = 20.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = -h_hop_s
h_cell = np.zeros((4*w, 4*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, 2*w:3*w] = h_hop_s
h_cell[w:2*w, w:2*w] = -h_cell_s
h_cell[w:2*w, 3*w:4*w] = -h_hop_s
h_cell[2*w:3*w, :w] = h_hop_s
h_cell[2*w:3*w, 2*w:3*w] = h_cell_s
h_cell[3*w:4*w, w:2*w] = -h_hop_s
h_cell[3*w:4*w, 3*w:4*w] = -h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = -np.conj(leads.square_selfenergy(w, t, e))
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_regular_degenerate_with_crossing():
"""This is a testcase with invertible hopping matrices,
and degenerate k-values with a crossing such that one
mode has a positive velocity, and one a negative velocity
For this case the fall-back technique must be used.
"""
w = 4 # width
t = 0.5 # hopping element
e = 1.8 # Fermi energy
global h_hop
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
hop = np.zeros((2*w, 2*w))
hop[:w, :w] = h_hop_s
hop[w:, w:] = -h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[w:, w:] = -h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = -np.conj(leads.square_selfenergy(w, t, e))
assert_almost_equal(g, modes_se(h_cell, hop))
def test_singular_fully_degenerate():
"""This testcase features a rectangular (and hence singular)
hopping matrix with complete degeneracy.
This case can still be treated with the Schur technique."""
w = 5 # width
t = 1.5 # hopping element
e = 3.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((4*w, 2*w))
h_hop[2*w:3*w, :w] = h_hop_s
h_hop[3*w:4*w, w:2*w] = h_hop_s
h_cell = np.zeros((4*w, 4*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, 2*w:3*w] = h_hop_s
h_cell[w:2*w, w:2*w] = h_cell_s
h_cell[w:2*w, 3*w:4*w] = h_hop_s
h_cell[2*w:3*w, :w] = h_hop_s
h_cell[2*w:3*w, 2*w:3*w] = h_cell_s
h_cell[3*w:4*w, w:2*w] = h_hop_s
h_cell[3*w:4*w, 3*w:4*w] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_regular_degenerate_with_crossing():
"""This is a testcase with invertible hopping matrices,
and degenerate k-values with a crossing such that one
mode has a positive velocity, and one a negative velocity
For this case the fall-back technique must be used.
"""
w = 4 # width
t = 0.5 # hopping element
e = 1.8 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
hop = np.zeros((2*w, 2*w))
hop[:w, :w] = h_hop_s
hop[w:, w:] = -h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[w:, w:] = -h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = -np.conj(leads.square_selfenergy(w, t, e))
assert_almost_equal(g, modes_se(h_cell, hop))
def test_singular_but_square():
"""This testcase features a singular, square hopping matrices
without degeneracies.
This case can be treated with the Schur technique."""
w = 5 # width
t = 0.9 # hopping element
e = 2.38 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[w:, :w] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, w:] = h_hop_s
h_cell[w:, :w] = h_hop_s
h_cell[w:, w:] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_analytic_numeric():
w = 5 # width
t = 0.78 # hopping element
e = 1.3 # Fermi energy
assert_almost_equal(leads.square_selfenergy(w, t, e),
modes_se(h_cell_s_func(t, w, e), -t * np.identity(w)))
def test_singular_but_square():
"""This testcase features a singular, square hopping matrices
without degeneracies.
This case can be treated with the Schur technique."""
w = 5 # width
t = 0.9 # hopping element
e = 2.38 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[w:, :w] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, w:] = h_hop_s
h_cell[w:, :w] = h_hop_s
h_cell[w:, w:] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_analytic_numeric():
w = 5 # width
t = 0.78 # hopping element
e = 1.3 # Fermi energy
assert_almost_equal(leads.square_selfenergy(w, t, e),
modes_se(h_cell_s_func(t, w, e), -t * np.identity(w)))
def test_regular_fully_degenerate():
"""Selfenergy with an invertible hopping matrix, and degenerate bands."""
w = 6 # width
t = 0.5 # hopping element
e = 1.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[:w, :w] = h_hop_s
h_hop[w:, w:] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[w:, w:] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
# Now with conservation laws and symmetries.
conserved = np.identity(2*w)
projectors = [sparse.csr_matrix(i) for i in [conserved[:, :w],
conserved[:, w:]]]
modes2 = leads.modes(h_cell, h_hop, projectors=projectors)
current_conserving(modes2[1])
assert_almost_equal(g, modes2[1].selfenergy())
trs = sparse.identity(2*w)
modes3 = leads.modes(h_cell, h_hop, projectors=projectors,
time_reversal=trs)
current_conserving(modes3[1])
assert_almost_equal(g, modes3[1].selfenergy())
phs = np.eye(2*w, 2*w, w) + np.eye(2*w, 2*w, -w)
modes4 = leads.modes(h_cell, h_hop, projectors=projectors,
time_reversal=trs, particle_hole=phs)
current_conserving(modes4[1])
assert_almost_equal(g, modes4[1].selfenergy())
def test_regular_fully_degenerate():
"""Selfenergy with an invertible hopping matrix, and degenerate bands."""
w = 6 # width
t = 0.5 # hopping element
e = 1.3 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, 2*w))
h_hop[:w, :w] = h_hop_s
h_hop[w:, w:] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[w:, w:] = h_cell_s
g = np.zeros((2*w, 2*w), dtype=complex)
g[:w, :w] = leads.square_selfenergy(w, t, e)
g[w:, w:] = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_singular():
"""This testcase features a rectangular (and hence singular)
hopping matrix without degeneracies.
This case can be treated with the Schur technique."""
w = 5 # width
t = .5 # hopping element
e = 0.4 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, w))
h_hop[w:, :w] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, w:] = h_hop_s
h_cell[w:, :w] = h_hop_s
h_cell[w:, w:] = h_cell_s
g = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def test_singular():
"""This testcase features a rectangular (and hence singular)
hopping matrix without degeneracies.
This case can be treated with the Schur technique."""
w = 5 # width
t = .5 # hopping element
e = 0.4 # Fermi energy
h_hop_s = -t * np.identity(w)
h_cell_s = h_cell_s_func(t, w, e)
h_hop = np.zeros((2*w, w))
h_hop[w:, :w] = h_hop_s
h_cell = np.zeros((2*w, 2*w))
h_cell[:w, :w] = h_cell_s
h_cell[:w, w:] = h_hop_s
h_cell[w:, :w] = h_hop_s
h_cell[w:, w:] = h_cell_s
g = leads.square_selfenergy(w, t, e)
assert_almost_equal(g, modes_se(h_cell, h_hop))
def selfenergy(self, fermi_energy, args=()):
return square_selfenergy(self.width, self.t,
self.potential + fermi_energy)
def selfenergy(self, fermi_energy, args=(), params=None):
assert not args
assert params is None
return square_selfenergy(self.width, self.t,
self.potential + fermi_energy)
def selfenergy(self, fermi_energy, args=()):
return square_selfenergy(self.width, self.t,
self.potential + fermi_energy)
