def plot_Peierls_Hubbard_green(u=0.0):
''' plot the Det(G) in the plane dt-w'''
L = 6
num = 51
d_num = 20
ws = np.linspace(-3, 3, num)
Gd = np.zeros((num, d_num), dtype=np.complex)
for j, d in enumerate(np.linspace(-1, 1, d_num)):
H = Peierls_Hubbard(L, t=1., dt=d, U=u, pbc=False)
evals, evecs = func.solve_hamiltonian(H)
Gwk = np.zeros(num, dtype=np.complex)
Gij_up = func.green(ws, op.fermion_up(), L, evals, evecs)
Gij_down = func.green(ws, op.fermion_down(), L, evals, evecs)
for i in range(num):
Gwk[i] = det(Gij_up[i]) * det(Gij_down[i])
Gd[:, j] = Gwk
# plt.figure("Green u=%.2f"%d)
# plt.plot(ws, np.real(Gwk),'o-')
# plt.ylim([-1,1])
# print np.min( np.imag(Gwk) ), np.max( np.imag(Gwk) )
plt.figure("poles")
fig = plt.imshow(np.real(Gd), interpolation='nearest', aspect=0.4)
fig.set_clim(-1, 1)
plt.colorbar(ticks=[-1, 0, 1], label="Det(G)")
plt.xticks([0.5, d_num / 2., d_num - 0.5], [-1, 0, 1], fontsize=20)
plt.yticks([0.5, num / 2., num - 0.5], [3, 0, -3], fontsize=20)
plt.xlabel('d', fontsize=20)
plt.ylabel('w', fontsize=20)
def plot_Peierls_Hubbard_green(u=0.0):
''' plot the Det(G) in the plane dt-w'''
L = 6
num = 51
d_num = 20
ws = np.linspace(-3,3,num)
Gd = np.zeros((num, d_num), dtype=np.complex)
for j, d in enumerate(np.linspace(-1,1,d_num)):
H = Peierls_Hubbard(L, t=1., dt=d, U=u, pbc=False)
evals, evecs = func.solve_hamiltonian(H)
Gwk = np.zeros(num, dtype=np.complex)
Gij_up = func.green(ws, op.fermion_up(), L, evals, evecs)
Gij_down = func.green(ws, op.fermion_down(), L, evals, evecs)
for i in range(num):
Gwk[i] = det(Gij_up[i])*det(Gij_down[i])
Gd[:,j] = Gwk
# plt.figure("Green u=%.2f"%d)
# plt.plot(ws, np.real(Gwk),'o-')
# plt.ylim([-1,1])
# print np.min( np.imag(Gwk) ), np.max( np.imag(Gwk) )
plt.figure("poles")
fig = plt.imshow(np.real(Gd), interpolation='nearest', aspect=0.4)
fig.set_clim(-1,1)
plt.colorbar(ticks=[-1,0,1],label="Det(G)")
plt.xticks([0.5,d_num/2.,d_num-0.5], [-1,0,1], fontsize=20)
plt.yticks([0.5,num/2.,num-0.5], [3,0,-3], fontsize=20)
plt.xlabel('d', fontsize=20)
plt.ylabel('w', fontsize=20)
def plot_Kitaev_green():
''' plot the Det(G) in the plane u-w'''
L = 8
num = 51
u_num = 20
ws = np.linspace(-3, 3, num)
Gd = np.zeros((num, u_num), dtype=np.complex)
for j, u in enumerate(np.linspace(0, 2, u_num)):
H = Kitaev(L, t=1., u=u, d=1., pbc=False)
evals, evecs = func.solve_hamiltonian(H)
Gwk = np.zeros(num, dtype=np.complex)
Gij = func.green(ws, op.fermion_c(), L, evals, evecs)
for i in range(num):
Gwk[i] = det(Gij[i])
Gd[:, j] = Gwk
plt.figure("poles")
fig = plt.imshow(np.real(Gd), interpolation='nearest', aspect=0.4)
fig.set_clim(-1, 1)
plt.colorbar(ticks=[-1, 0, 1], label="Det(G)")
plt.xticks([0.5, u_num / 2., u_num - 0.5], [0, 1, 2], fontsize=20)
plt.yticks([0.5, num / 2., num - 0.5], [3, 0, -3], fontsize=20)
plt.xlabel('u', fontsize=20)
plt.ylabel('w', fontsize=20)
def plot_Hubbard_green_wk():
L = 6
H = Hubbard(L, t=1., u=1., f=1., pbc=True)
evals, evecs = func.solve_hamiltonian(H)
sec = 0
ge = evals[0][0]
for s in range(evals.shape[0]):
if evals[s][0] < ge:
ge = evals[s][0]
sec = s
num = op.fermion_up().hermitian().mult(op.fermion_up())
num.plus(op.fermion_down().hermitian().mult(op.fermion_down()))
density = func.expectation(L, evecs[sec][:, 0], sec, [num])
num = 11
ws = np.linspace(-3, 3, num)
Gij = func.green(ws, op.fermion_up(), L, evals, evecs)
Gwk = np.zeros((num, L + 1), dtype=np.complex)
for i in range(num):
Gwk[i, :] = func.fourier(Gij[i][0, :])
print Gij[(num - 1) / 2][0, :]
print func.fourier(Gij[(num - 1) / 2][0, :])
plt.figure("Green")
plt.imshow(np.imag(Gwk), interpolation='nearest', aspect='auto')
plt.colorbar()
print "density of the state:", density
def plot_SSH_green_wk(dt=1.):
''' plot the greens function in the k-w plane '''
L = 12
num = 51 # number of energies to calculate
ws = np.linspace(-3, 3, num)
H = SSH(L, t=1., d=dt, pbc=True)
evals, evecs = func.solve_hamiltonian(H)
f, ax = plt.subplots(2, 2) #, sharex='col', sharey='row')
d_num = L / 2 + 1
Gij = func.green(ws, op.fermion_c(), L, evals, evecs)
lim = 2
cdict = {
'red': [(0.0, 0.0, 0.0), (0.5, 1.0, 1.0), (1.0, 1.0, 1.0)],
'green': [(0.0, 0.0, 0.0), (0.5, 1.0, 1.0), (1.0, 0.0, 0.0)],
'blue': [(0.0, 1.0, 1.0), (0.5, 1.0, 1.0), (1.0, 0.0, 0.0)]
}
from matplotlib.colors import LinearSegmentedColormap
cmap = LinearSegmentedColormap('mycm', cdict)
for x1 in range(2):
for x2 in range(2):
Gd = np.zeros((num, d_num), dtype=np.complex)
for i in range(num):
Gd[i, :] = func.fourier(Gij[i][x1, x2::2])
# plt.figure("%d-%d"%(x1,x2))
im = ax[x1][x2].imshow(np.real(Gd),
interpolation='nearest',
origin='lower',
extent=(0, np.pi * 2, -3., 3.),
aspect='auto',
cmap=cmap)
im.set_clim(-lim, lim)
def plot_Kitaev_green():
''' plot the Det(G) in the plane u-w'''
L = 8
num = 51
u_num = 20
ws = np.linspace(-3,3,num)
Gd = np.zeros((num, u_num), dtype=np.complex)
for j, u in enumerate(np.linspace(0,2,u_num)):
H = Kitaev(L, t=1., u=u, d=1., pbc=False)
evals, evecs = func.solve_hamiltonian(H)
Gwk = np.zeros(num, dtype=np.complex)
Gij = func.green(ws, op.fermion_c(), L, evals, evecs)
for i in range(num):
Gwk[i] = det(Gij[i])
Gd[:,j] = Gwk
plt.figure("poles")
fig = plt.imshow(np.real(Gd), interpolation='nearest', aspect=0.4)
fig.set_clim(-1,1)
plt.colorbar(ticks=[-1,0,1],label="Det(G)")
plt.xticks([0.5,u_num/2.,u_num-0.5], [0,1,2], fontsize=20)
plt.yticks([0.5,num/2.,num-0.5], [3,0,-3], fontsize=20)
plt.xlabel('u', fontsize=20)
plt.ylabel('w', fontsize=20)
def plot_Hubbard_green_wk():
L=6
H = Hubbard(L, t=1., u=1., f=1., pbc=True)
evals, evecs = func.solve_hamiltonian(H)
sec= 0
ge = evals[0][0]
for s in range(evals.shape[0]):
if evals[s][0] < ge:
ge = evals[s][0]
sec = s
num = op.fermion_up().hermitian().mult( op.fermion_up() )
num.plus( op.fermion_down().hermitian().mult( op.fermion_down() ) )
density = func.expectation(L, evecs[sec][:,0], sec, [num] )
num = 11
ws = np.linspace(-3,3,num)
Gij = func.green(ws, op.fermion_up(), L, evals, evecs)
Gwk = np.zeros((num, L+1), dtype=np.complex)
for i in range(num):
Gwk[i, :] = func.fourier(Gij[i][0,:])
print Gij[(num-1)/2][0,:]
print func.fourier(Gij[(num-1)/2][0,:])
plt.figure("Green")
plt.imshow(np.imag(Gwk), interpolation='nearest', aspect='auto')
plt.colorbar()
print "density of the state:", density
def plot_SSH_green_wk(dt=1.):
''' plot the greens function in the k-w plane '''
L = 12
num = 51 # number of energies to calculate
ws = np.linspace(-3,3,num)
H = SSH(L, t=1., d=dt, pbc=True)
evals, evecs = func.solve_hamiltonian(H)
f, ax = plt.subplots(2,2)#, sharex='col', sharey='row')
d_num = L/2+1
Gij = func.green(ws, op.fermion_c(), L, evals, evecs)
lim = 2
cdict = {'red': [(0.0, 0.0, 0.0), (0.5, 1.0, 1.0), (1.0, 1.0, 1.0)],
'green': [(0.0, 0.0, 0.0), (0.5, 1.0, 1.0), (1.0, 0.0, 0.0)],
'blue': [(0.0, 1.0, 1.0), (0.5, 1.0, 1.0), (1.0, 0.0, 0.0)]}
from matplotlib.colors import LinearSegmentedColormap
cmap = LinearSegmentedColormap('mycm', cdict)
for x1 in range(2):
for x2 in range(2):
Gd = np.zeros((num, d_num), dtype=np.complex)
for i in range(num):
Gd[i, :] = func.fourier(Gij[i][x1,x2::2])
# plt.figure("%d-%d"%(x1,x2))
im = ax[x1][x2].imshow(np.real(Gd), interpolation='nearest', origin='lower',
extent=(0,np.pi*2,-3.,3.), aspect='auto', cmap=cmap)
im.set_clim(-lim,lim)