# Add the root path of the pygra library import os import sys sys.path.append(os.environ['PYGRAROOT']) # zigzag ribbon import numpy as np from pygra import geometry from pygra import scftypes from pygra import operators from scipy.sparse import csc_matrix g = geometry.honeycomb_lattice() h = g.get_hamiltonian() # create hamiltonian of the system h.add_anti_kane_mele(0.1) mf = scftypes.guess(h, mode="random") # antiferro initialization # perform SCF with specialized routine for Hubbard U = 3.0 scf = scftypes.hubbardscf(h, nkp=10, filling=0.5, g=U, mix=0.9, mf=mf) scf.hamiltonian.get_bands(operator="sz")
# Add the root path of the pygra library import os import sys sys.path.append(os.environ['PYGRAROOT']) # zigzag ribbon from pygra import geometry from pygra import scftypes g = geometry.honeycomb_zigzag_ribbon(10) # create geometry of a zigzag ribbon h = g.get_hamiltonian() # create hamiltonian of the system mf = scftypes.guess(h, "ferro", fun=lambda r: [0., 0., 1.]) scf = scftypes.hubbardscf(h, nkp=30, filling=0.5, mf=mf) h = scf.hamiltonian # get the Hamiltonian h.get_bands(operator="sz") # calculate band structure
is_multicell=False,
mgenerator=specialhopping.twisted_matrix(ti=0.5,
lambi=7.0))
h.turn_dense()
#def ff(r):
# return 0.2*r[2]
#h.shift_fermi(ff)
h.turn_spinful()
h.turn_dense()
h.add_sublattice_imbalance(0.5)
h.add_kane_mele(0.03)
#h.get_bands(num_bands=40)
#exit()
from pygra import meanfield
mf = meanfield.guess(h, "antiferro", 0.1)
g = 2.0
filling = 0.5 + 1. / h.intra.shape[0] # plus two electrons
nk = 1
scf = scftypes.hubbardscf(h,
nkp=nk,
filling=filling,
g=g,
mix=0.9,
mf=mf,
maxite=1)
#scf1 = scftypes.selfconsistency(h,nkp=nk,filling=0.5,g=g,
# mix=0.9,mf=mf)
scf.hamiltonian.get_bands(num_bands=40, operator="sz")
#print(scf.total_energy-scf1.total_energy)
f = open("ENERGY_VS_ANGLE.OUT", "w") # file with the results
for p in ps: # loop over angles
h = h0.copy() # copy Hamiltonian
# the following will rotate the spin quantization axis in the
# unit cell, so that we can fix the magnetization along one
# direction and compute the magnetic anisotropy
# the angle is given in units of pi, i.e. p=0.5 is 90 degrees
h.global_spin_rotation(angle=p, vector=[1., 0., 0.])
U = 3.0 # large U to get antiferromagnetism
# antiferro initialization
mf = scftypes.guess(h, mode="antiferro", fun=lambda x: 1.0)
# perform SCF with specialized routine for collinear Hubbard
scf = scftypes.hubbardscf(h,
nkp=5,
filling=0.5,
g=U,
mix=0.5,
mf=mf,
collinear=True)
e = scf.total_energy # get the energy of the system
es.append(e) # store energy
f.write(str(p) + " " + str(e) + "\n") # write in the file
f.close() # close the file
## Plot the energies ##
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams.update({'font.size': 18})
matplotlib.rcParams['font.family'] = "Bitstream Vera Serif"
fig = plt.figure()
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src")
from pygra import islands
from pygra import interactions
from pygra import scftypes
import numpy as np
g = islands.get_geometry(name="honeycomb",
n=40,
nedges=3,
rot=np.pi / 3,
clean=False) # get an island
g.write()
exit()
h = g.get_hamiltonian() # get the Hamiltonian
scf = scftypes.hubbardscf(h, g=1.0, mag=[[0, 0, 1] for r in g.r])
scf.hamiltonian.get_bands()
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.environ['PYGRAROOT'])
# zigzag ribbon
from pygra import geometry
from pygra import scftypes
import numpy as np
# this spin calculates the spin stiffness of an interacting 1d chain
g = geometry.chain() # chain geometry
h0 = g.get_hamiltonian() # create hamiltonian of the system
fo = open("STIFFNESS.OUT", "w") # open file
for a in np.linspace(0., .2, 20): # loop over angles, in units of pi
h = h0.copy()
h.generate_spin_spiral(angle=a, vector=[0., 1., 0.])
scf = scftypes.hubbardscf(h,
filling=0.1,
nkp=100,
g=2.5,
silent=True,
mag=[[0., 0., .1]],
mix=0.9,
maxerror=1e-4)
fo.write(str(a) + " " + str(scf.total_energy) + "\n") # write
print(a, scf.total_energy)
fo.close()
# zigzag ribbon
import numpy as np
from pygra import geometry
from pygra import scftypes
from pygra import operators
from scipy.sparse import csc_matrix
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
U = 5.0
mf = scftypes.guess(h,mode="antiferro") # antiferro initialization
# perform SCF with specialized routine for Hubbard
# save = True will write the mean field in a file at every iteration
scf = scftypes.hubbardscf(h,nkp=20,filling=0.5,g=U,
mix=0.9,mf=mf,save=True,silent=True)
# perform it again without giving a MF (it will be read from a file)
# mf = None forces the code to read the mean field from a file
scf = scftypes.hubbardscf(h,nkp=20,filling=0.5,g=U,
mix=0.9,mf=None,save=True)
for p in ps: # loop over angles
h = h0.copy() # copy Hamiltonian
h.add_kane_mele(p) # Add Kane-Mele SOC
hoff = h.copy()
hin = h.copy()
# Hamiltonian with in-plane quantization axis
hin.global_spin_rotation(angle=0.5,vector=[1.,0.,0.])
U = 3.0 # large U to get antiferromagnetism
# offplane antiferro initialization
mfoff = scftypes.guess(h,mode="antiferro",fun = lambda x: [0.,0.,1.0])
# inplane antiferro initialization
mfin = scftypes.guess(h,mode="antiferro",fun = lambda x: [1.0,0.,0.])
# compute the energies using collinear formalism with different
# quantization axis. In this case, the collinear formalism
# will enforce the magnetization in the z direction
scfoff = scftypes.hubbardscf(hoff,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=True)
scfin = scftypes.hubbardscf(hin,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=True)
# alternatively, we can use a non-collinear formalism and go to the
# ground state with using two different initializations
# compute energies using non-collinear formalism but different initialization
scfoff2 = scftypes.hubbardscf(h,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=False)
scfin2 = scftypes.hubbardscf(h,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfin,collinear=False)
# Now compute energy differences
e0 = scfoff.total_energy - scfin.total_energy
e1 = scfoff2.total_energy - scfin2.total_energy
# and store the energies
es0.append(e0) # store energy
es1.append(e1) # store energy
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.environ['PYGRAROOT'])
# zigzag ribbon
import numpy as np
from pygra import geometry
from pygra import scftypes
from pygra import parallel
parallel.cores = 7
from scipy.sparse import csc_matrix
g = geometry.honeycomb_lattice()
g.write()
Us = np.linspace(0., 4., 10) # different Us
#f = open("EVOLUTION.OUT","w") # file with the results
h = g.get_hamiltonian() # create hamiltonian of the system
mf = scftypes.guess(h, mode="antiferro") # antiferro initialization
# perform SCF with specialized routine for Hubbard
U = 3.0
scf = scftypes.hubbardscf(h, nkp=20, filling=0.5, g=U, mix=0.001, mf=mf)
from pygra import specialgeometry
from pygra import scftypes
g = specialgeometry.twisted_bilayer(8)
#g = geometry.honeycomb_lattice()
g.write()
from pygra import specialhopping
h = g.get_hamiltonian(is_sparse=True,has_spin=False,is_multicell=False,
mgenerator=specialhopping.twisted_matrix(ti=0.5,lambi=7.0))
h.turn_dense()
#def ff(r):
# return 0.2*r[2]
#h.shift_fermi(ff)
h.turn_spinful()
h.turn_dense()
h.add_sublattice_imbalance(0.5)
h.add_kane_mele(0.03)
#h.get_bands(num_bands=40)
#exit()
from pygra import meanfield
mf = meanfield.guess(h,"antiferro",0.1)
g = 2.0
filling = 0.5 + 1./h.intra.shape[0] # plus two electrons
nk = 1
scf = scftypes.hubbardscf(h,nkp=nk,filling=filling,g=g,
mix=0.9,mf=mf,maxite=1)
#scf1 = scftypes.selfconsistency(h,nkp=nk,filling=0.5,g=g,
# mix=0.9,mf=mf)
scf.hamiltonian.get_bands(num_bands=40,operator="sz")
#print(scf.total_energy-scf1.total_energy)
# Add the root path of the pygra library
import os ; import sys ; sys.path.append(os.environ['PYGRAROOT'])
# zigzag ribbon
import numpy as np
from pygra import geometry
from pygra import scftypes
from pygra import operators
from scipy.sparse import csc_matrix
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
U = 5.0
mf = scftypes.guess(h,mode="antiferro") # antiferro initialization
# perform SCF with specialized routine for Hubbard
# save = True will write the mean field in a file at every iteration
scf = scftypes.hubbardscf(h,nkp=20,filling=0.5,g=U,
mix=0.9,mf=mf,save=True,silent=True)
# perform it again without giving a MF (it will be read from a file)
# mf = None forces the code to read the mean field from a file
scf = scftypes.hubbardscf(h,nkp=20,filling=0.5,g=U,
mix=0.9,mf=None,save=True)
# Add the root path of the pygra library
import os ; import sys ; sys.path.append(os.environ['PYGRAROOT'])
# zigzag ribbon
import numpy as np
from pygra import geometry
from pygra import scftypes
from pygra import operators
from scipy.sparse import csc_matrix
g = geometry.honeycomb_lattice()
g.write()
Us = np.linspace(0.,4.,10) # different Us
f = open("EVOLUTION.OUT","w") # file with the results
for U in Us: # loop over Us
h = g.get_hamiltonian() # create hamiltonian of the system
mf = scftypes.guess(h,mode="antiferro") # antiferro initialization
# perform SCF with specialized routine for Hubbard
scf = scftypes.hubbardscf(h,nkp=20,filling=0.5,g=U,
mix=0.9,mf=mf)
# alternatively use
# scf = scftypes.selfconsistency(h,nkp=20,filling=0.5,g=U,
# mix=0.9,mf=mf)
h = scf.hamiltonian # get the Hamiltonian
gap = h.get_gap() # compute the gap
f.write(str(U)+" "+str(gap)+"\n")
f.close()
for p in ps: # loop over angles
h = h0.copy() # copy Hamiltonian
h.add_kane_mele(p) # Add Kane-Mele SOC
hoff = h.copy()
hin = h.copy()
# Hamiltonian with in-plane quantization axis
hin.global_spin_rotation(angle=0.5,vector=[1.,0.,0.])
U = 3.0 # large U to get antiferromagnetism
# offplane antiferro initialization
mfoff = scftypes.guess(h,mode="antiferro",fun = lambda x: [0.,0.,1.0])
# inplane antiferro initialization
mfin = scftypes.guess(h,mode="antiferro",fun = lambda x: [1.0,0.,0.])
# compute the energies using collinear formalism with different
# quantization axis. In this case, the collinear formalism
# will enforce the magnetization in the z direction
scfoff = scftypes.hubbardscf(hoff,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=True)
scfin = scftypes.hubbardscf(hin,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=True)
# print(scfoff.total_energy)
# print(scfin.total_energy)
# exit()
# alternatively, we can use a non-collinear formalism and go to the
# ground state with using two different initializations
# compute energies using non-collinear formalism but different initialization
scfoff2 = scftypes.hubbardscf(h,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfoff,collinear=False)
scfin2 = scftypes.hubbardscf(h,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mfin,collinear=False)
# Now compute energy differences
e0 = scfoff.total_energy - scfin.total_energy
e1 = scfoff2.total_energy - scfin2.total_energy
es = [] # empty list for the total energies
f = open("ENERGY_VS_ANGLE.OUT","w") # file with the results
for p in ps: # loop over angles
h = h0.copy() # copy Hamiltonian
# the following will rotate the spin quantization axis in the
# unit cell, so that we can fix the magnetization along one
# direction and compute the magnetic anisotropy
# the angle is given in units of pi, i.e. p=0.5 is 90 degrees
h.global_spin_rotation(angle=p,vector=[1.,0.,0.])
U = 3.0 # large U to get antiferromagnetism
# antiferro initialization
mf = scftypes.guess(h,mode="antiferro",fun = lambda x: 1.0)
# perform SCF with specialized routine for collinear Hubbard
scf = scftypes.hubbardscf(h,nkp=5,filling=0.5,g=U,
mix=0.5,mf=mf,collinear=True)
e = scf.total_energy # get the energy of the system
es.append(e) # store energy
f.write(str(p)+" "+str(e)+"\n") # write in the file
f.close() # close the file
## Plot the energies ##
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams.update({'font.size': 18})
matplotlib.rcParams['font.family'] = "Bitstream Vera Serif"
fig = plt.figure()
fig.subplots_adjust(0.2,0.2)
plt.plot(ps*180,es,marker="o",c="blue")
