def get_chik(k): # function which returns a matrix """ Get response at a cetain energy""" hk = hkgen(k) # first point if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component e1,ev1 = lg.eigh(hk) # get eigenvalues hk = hkgen(k+q) # second point if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component e2,ev2 = lg.eigh(hk) # get eigenvalues ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution return ct # return response
def get_chik(k): # function which returns a matrix """ Get response at a cetain energy""" hk = hkgen(k) # first point if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component e1,ev1 = lg.eigh(hk) # get eigenvalues hk = hkgen(k+q) # second point if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component e2,ev2 = lg.eigh(hk) # get eigenvalues ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution return ct # return response
def get_chik(k):
"""Function to integrate"""
hk = hkgen(k) # fist point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
if collinear:
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
else:
ct = calculate_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
return ct
def get_chik(k):
"""Function to integrate"""
hk = hkgen(k) # fist point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
if collinear:
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
else:
ct = calculate_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
return ct
def collinear_chi1d(h,energies = [0.],t=0.0001,delta=0.01,q=0.001,nk=1000,U=None,adaptive=True,ks=None):
collinear = True
hkgen = h.get_hk_gen() # get the generating hamiltonian
n = len(h.geometry.x) # initialice response
m = np.zeros((len(energies),n*n),dtype=np.complex) # initialice
if not adaptive: # full algorithm
if ks==None: ks = np.linspace(0.,1.,nk) # create klist
for k in ks:
# print "Doing k=",k
hk = hkgen(k) # fist point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
m += ct
m = m/nk # normalice by the number of kpoints
ms = [m[i,:].reshape(n,n) for i in range(len(m))] # convert to matrices
if adaptive: # adaptive algorithm
from integration import integrate_matrix
def get_chik(k): # function which returns a matrix
""" Get response at a cetain energy"""
hk = hkgen(k) # first point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
return ct # return response
ms = []
m = integrate_matrix(get_chik,xlim=[0.,1.],eps=.01,only_imag=False) # add energy
ms = [m[i,:].reshape(n,n) for i in range(len(m))] # convert to matrices
if U==None: # raw calculation
return ms
else: # RPA calculation
return rpachi(ms,U=U)
def collinear_chi1d(h,energies = [0.],t=0.0001,delta=0.01,q=0.001,nk=1000,U=None,adaptive=True,ks=None):
collinear = True
hkgen = h.get_hk_gen() # get the generating hamiltonian
n = len(h.geometry.x) # initialice response
m = np.zeros((len(energies),n*n),dtype=np.complex) # initialice
if not adaptive: # full algorithm
if ks==None: ks = np.linspace(0.,1.,nk) # create klist
for k in ks:
# print "Doing k=",k
hk = hkgen(k) # fist point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
m += ct
m = m/nk # normalice by the number of kpoints
ms = [m[i,:].reshape(n,n) for i in range(len(m))] # convert to matrices
if adaptive: # adaptive algorithm
from integration import integrate_matrix
def get_chik(k): # function which returns a matrix
""" Get response at a cetain energy"""
hk = hkgen(k) # first point
if collinear: hk = np.matrix([[hk[2*i,2*j] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # up component
e1,ev1 = lg.eigh(hk) # get eigenvalues
hk = hkgen(k+q) # second point
if collinear: hk = np.matrix([[hk[2*i+1,2*j+1] for i in range(len(hk)/2)] for j in range(len(hk)/2)]) # down component
e2,ev2 = lg.eigh(hk) # get eigenvalues
ct = collinear_xychi(ev1.T,e1,ev2.T,e2,energies,t,delta) # contribution
return ct # return response
ms = []
m = integrate_matrix(get_chik,xlim=[0.,1.],eps=.01,only_imag=False) # add energy
ms = [m[i,:].reshape(n,n) for i in range(len(m))] # convert to matrices
if U==None: # raw calculation
return ms
else: # RPA calculation
return rpachi(ms,U=U)
