def Self_Consistency(self) :
S.Transform_SymmetryBasis_toRealSpace (IN= S.Sigma, OUT = Sigma) # Embedding
# Computes sum over BZ and returns density
F = lambda mu : SK(mu = mu,Sigma = Sigma, Field = None ,Res = G).total_density()/4
if Density_Required :
self.Chemical_potential = Dichotomy.Dichotomy(Function = F,
xinit = self.Chemical_potential, yvalue =Density_Required,
Precision_on_y = 0.01, Delta_x=0.5, MaxNbreLoop = 100,
xname="Chemical_Potential", yname= "Total Density",
verbosity = 3)[0]
else:
MPI.report("Total density = %.3f"%F(self.Chemical_potential))
S.Transform_RealSpace_to_SymmetryBasis (IN = G, OUT = S.G) # Extraction
S.G0 = inverse(S.Sigma + inverse(S.G)) # Finally get S.G0
def GF_realomega(self,ommin,ommax,N_om,broadening=0.01):
"""Calculates the GF and spectral function on the real axis."""
delta_om = (ommax-ommin)/(1.0*(N_om-1))
omega = numpy.zeros([N_om],numpy.complex_)
Mesh = numpy.zeros([N_om],numpy.float_)
for i in range(N_om):
omega[i] = ommin + delta_om * i + 1j * broadening
Mesh[i] = ommin + delta_om * i
temp = 1.0/self.Beta
gf,tail,self.atocc,self.atmag = gf_hi_fullu(e0f=self.ealmat, ur=self.ur, umn=self.umn, ujmn=self.ujmn,
zmsb=omega, nmom=self.Nmoments, ns=self.Nspin, temp=temp, verbosity = self.Verbosity)
for sig in self.a_list:
for i in range(11): self.tailtempl[sig][i].array[:] *= 0.0
# transfer the data to the GF class:
if (self.UseSpinOrbit):
nlmtot = self.Nlm*2 # only one block in this case!
else:
nlmtot = self.Nlm
M={}
isp=-1
for a,al in self.GFStruct:
isp+=1
#M[a] = gf[isp*self.Nlm:(isp+1)*self.Nlm,isp*self.Nlm:(isp+1)*self.Nlm,:]
M[a] = gf[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot,:]
for i in range(min(self.Nmoments,10)):
self.tailtempl[a][i+1].array[:] = tail[i][isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot]
glist = lambda : [ GFBloc_ReFreq(Indices = al, Beta = self.Beta, MeshArray = Mesh, Data=M[a], Tail=self.tailtempl[a])
for a,al in self.GFStruct] # Indices for the upfolded G
self.G = GF(NameList = self.a_list, BlockList = glist(),Copy=False)
# Self energy:
self.G0 = self.G.copy()
self.Sigma = self.G.copy()
self.G0 <<= GF_Initializers.A_Omega_Plus_B(A=1,B=1j*broadening)
M = [ self.ealmat[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot] for isp in range((2*self.Nlm)/nlmtot) ]
self.G0 -= M
self.Sigma <<= self.G0 - inverse(self.G)
self.Sigma.Note='ReFreq' # This is important for the put_Sigma routine!!!
def Self_Consistency(self):
S.Transform_SymmetryBasis_toRealSpace(IN=S.Sigma,
OUT=Sigma) # Embedding
# Computes sum over BZ and returns density
F = lambda mu: SK(mu=mu, Sigma=Sigma, Field=None, Res=G).total_density(
) / 4
if Density_Required:
self.Chemical_potential = Dichotomy.Dichotomy(
Function=F,
xinit=self.Chemical_potential,
yvalue=Density_Required,
Precision_on_y=0.01,
Delta_x=0.5,
MaxNbreLoop=100,
xname="Chemical_Potential",
yname="Total Density",
verbosity=3)[0]
else:
MPI.report("Total density = %.3f" % F(self.Chemical_potential))
S.Transform_RealSpace_to_SymmetryBasis(IN=G, OUT=S.G) # Extraction
S.G0 = inverse(S.Sigma + inverse(S.G)) # Finally get S.G0
def Self_Consistency(G0,G):
G0['0'] <<= inverse(Omega - (t**2)*G['0'])
# Import the Green's functions from pytriqs.Base.GF_Local import GFBloc_ImFreq, iOmega_n, inverse # Create the Matsubara-frequency Green's function and initialize it g = GFBloc_ImFreq(Indices = [1], Beta = 50, NFreqMatsubara = 1000, Name = "imp") g <<= inverse( iOmega_n + 0.5 ) from pytriqs.Base.Plot.MatplotlibInterface import oplot oplot(g, '-o', x_window = (0,10))
from pytriqs.Base.Plot.MatplotlibInterface import oplot
from pytriqs.Base.GF_Local import GFBloc_ImFreq, Omega, inverse
g = GFBloc_ImFreq(Indices=[1], Beta=300, NFreqMatsubara=1000, Name="g")
g <<= inverse(Omega + 0.5)
# the data we want to fit...
# The green function for omega \in [0,0.2]
X, Y = g.x_data_view(x_window=(0, 0.2), flatten_y=True)
from pytriqs.Base.Fit.fit import Fit, linear, quadratic
fitl = Fit(X, Y.imag, linear)
fitq = Fit(X, Y.imag, quadratic)
oplot(g, '-o', x_window=(0, 5))
oplot(fitl, '-x', x_window=(0, 0.5))
oplot(fitq, '-x', x_window=(0, 1))
# a bit more complex, we want to fit with a one fermion level ....
# Cf the definition of linear and quadratic in the lib
one_fermion_level = lambda X, a, b: 1 / (a * X * 1j + b
), r"${1}/(%f x + %f)$", (1, 1)
fit1 = Fit(X, Y, one_fermion_level)
oplot(fit1, '-x', x_window=(0, 3))
def Solve(self,Iteration_Number=1,Test_Convergence=0.0001):
"""Calculation of the impurity Greens function using Hubbard-I"""
# Test all a parameters before solutions
print Parameters.check(self.__dict__,self.Required,self.Optional)
#Solver_Base.Solve(self,is_last_iteration,Iteration_Number,Test_Convergence)
if self.Converged :
MPI.report("Solver %(Name)s has already converted: SKIPPING"%self.__dict__)
return
self.__save_eal('eal.dat',Iteration_Number)
MPI.report( "Starting Fortran solver %(Name)s"%self.__dict__)
self.Sigma_Old <<= self.Sigma
self.G_Old <<= self.G
# call the fortran solver:
temp = 1.0/self.Beta
gf,tail,self.atocc,self.atmag = gf_hi_fullu(e0f=self.ealmat, ur=self.ur, umn=self.umn, ujmn=self.ujmn,
zmsb=self.zmsb, nmom=self.Nmoments, ns=self.Nspin, temp=temp, verbosity = self.Verbosity)
#self.sig = sigma_atomic_fullu(gf=self.gf,e0f=self.eal,zmsb=self.zmsb,ns=self.Nspin,nlm=self.Nlm)
if (self.Verbosity==0):
# No fortran output, so give basic results here
MPI.report("Atomic occupancy in Hubbard I Solver : %s"%self.atocc)
MPI.report("Atomic magn. mom. in Hubbard I Solver : %s"%self.atmag)
# transfer the data to the GF class:
if (self.UseSpinOrbit):
nlmtot = self.Nlm*2 # only one block in this case!
else:
nlmtot = self.Nlm
M={}
isp=-1
for a,al in self.GFStruct:
isp+=1
#M[a] = gf[isp*self.Nlm:(isp+1)*self.Nlm,isp*self.Nlm:(isp+1)*self.Nlm,:]
M[a] = gf[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot,:]
for i in range(min(self.Nmoments,10)):
self.tailtempl[a][i+1].array[:] = tail[i][isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot]
glist = lambda : [ GFBloc_ImFreq(Indices = al, Beta = self.Beta, NFreqMatsubara = self.Nmsb, Data=M[a], Tail=self.tailtempl[a])
for a,al in self.GFStruct]
self.G = GF(NameList = self.a_list, BlockList = glist(),Copy=False)
# Self energy:
self.G0 <<= GF_Initializers.A_Omega_Plus_B(A=1,B=0.0)
M = [ self.ealmat[isp*nlmtot:(isp+1)*nlmtot,isp*nlmtot:(isp+1)*nlmtot] for isp in range((2*self.Nlm)/nlmtot) ]
self.G0 -= M
self.Sigma <<= self.G0 - inverse(self.G)
# invert G0
self.G0.invert()
def test_distance(G1,G2, dist) :
def f(G1,G2) :
print abs(G1._data.array - G2._data.array)
dS = max(abs(G1._data.array - G2._data.array).flatten())
aS = max(abs(G1._data.array).flatten())
return dS <= aS*dist
return reduce(lambda x,y : x and y, [f(g1,g2) for (i1,g1),(i2,g2) in izip(G1,G2)])
MPI.report("\nChecking Sigma for convergence...\nUsing tolerance %s"%Test_Convergence)
self.Converged = test_distance(self.Sigma,self.Sigma_Old,Test_Convergence)
if self.Converged :
MPI.report("Solver HAS CONVERGED")
else :
MPI.report("Solver has not yet converged")
# Import the Green's functions from pytriqs.Base.GF_Local import GFBloc_ImFreq, iOmega_n, inverse # Create the Matsubara-frequency Green's function and initialize it g = GFBloc_ImFreq(Indices=[1], Beta=50, NFreqMatsubara=1000, Name="imp") g <<= inverse(iOmega_n + 0.5) from pytriqs.Base.Plot.MatplotlibInterface import oplot oplot(g, '-o', x_window=(0, 10))
from pytriqs.Base.GF_Local import GFBloc_ReFreq, Omega, Wilson, inverse import numpy a = numpy.arange(-1.99,2.00,0.02) # Define the energy array eps_d,V = 0.3, 0.2 # Create the real-frequency Green's function and initialize it g = GFBloc_ReFreq(Indices = ['s','d'], Beta = 50, MeshArray = a, Name = "s+d") g['d','d'] = Omega - eps_d g['d','s'] = V g['s','d'] = V g['s','s'] = inverse( Wilson(1.0) ) g.invert() # Plot it with matplotlib. 'S' means: spectral function ( -1/pi Imag (g) ) from pytriqs.Base.Plot.MatplotlibInterface import oplot oplot( g['d','d'], '-o', RI = 'S', x_window = (-1.8,1.8), Name = "Impurity" ) oplot( g['s','s'], '-x', RI = 'S', x_window = (-1.8,1.8), Name = "Bath" )
from pytriqs.Base.Plot.MatplotlibInterface import oplot
from pytriqs.Base.GF_Local import GFBloc_ImFreq, Omega, inverse
g = GFBloc_ImFreq(Indices = [1], Beta = 300, NFreqMatsubara = 1000, Name = "g")
g <<= inverse( Omega + 0.5 )
# the data we want to fit...
# The green function for omega \in [0,0.2]
X,Y = g.x_data_view (x_window = (0,0.2), flatten_y = True )
from pytriqs.Base.Fit.fit import Fit, linear, quadratic
fitl = Fit ( X,Y.imag, linear )
fitq = Fit ( X,Y.imag, quadratic )
oplot (g, '-o', x_window = (0,5) )
oplot (fitl , '-x', x_window = (0,0.5) )
oplot (fitq , '-x', x_window = (0,1) )
# a bit more complex, we want to fit with a one fermion level ....
# Cf the definition of linear and quadratic in the lib
one_fermion_level = lambda X, a,b : 1/(a * X *1j + b), r"${1}/(%f x + %f)$" , (1,1)
fit1 = Fit ( X,Y, one_fermion_level )
oplot (fit1 , '-x', x_window = (0,3) )
from pytriqs.Base.GF_Local import GFBloc_ReFreq, Omega, Wilson, inverse import numpy a = numpy.arange(-1.99, 2.00, 0.02) # Define the energy array eps_d, V = 0.3, 0.2 # Create the real-frequency Green's function and initialize it g = GFBloc_ReFreq(Indices=['s', 'd'], Beta=50, MeshArray=a, Name="s+d") g['d', 'd'] = Omega - eps_d g['d', 's'] = V g['s', 'd'] = V g['s', 's'] = inverse(Wilson(1.0)) g.invert() # Plot it with matplotlib. 'S' means: spectral function ( -1/pi Imag (g) ) from pytriqs.Base.Plot.MatplotlibInterface import oplot oplot(g['d', 'd'], '-o', RI='S', x_window=(-1.8, 1.8), Name="Impurity") oplot(g['s', 's'], '-x', RI='S', x_window=(-1.8, 1.8), Name="Bath")
