def test_1(self):
g = geometry.honeycomb_lattice()
g = g.supercell(2)
k = np.random.random(3)
h1 = geth(3,1,g).get_hk_gen()(k)
h2 = geth(1,3,g).get_hk_gen()(k)
diff = np.max(np.abs(h1-h2))
print("Error = ",diff)
passed = diff<error
self.assertTrue(passed)
def test_1(self):
g = geometry.honeycomb_lattice()
g = g.supercell(2)
k = np.random.random(3)
h1 = geth(3, 1, g).get_hk_gen()(k)
h2 = geth(1, 3, g).get_hk_gen()(k)
diff = np.max(np.abs(h1 - h2))
print("Error = ", diff)
passed = diff < error
self.assertTrue(passed)
def func_to_parallelize(U):
"""Function to parallelize"""
# all the variables must be internal!
from pygra import geometry
from pygra import meanfield
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
mf = meanfield.guess(h,mode="antiferro") # antiferro initialization
# perform SCF with specialized routine for Hubbard
scf = meanfield.hubbardscf(h,nk=20,filling=0.5,U=U,verbose=1,
mix=0.9,mf=mf)
# alternatively use
h = scf.hamiltonian # get the Hamiltonian
gap = h.get_gap() # compute the gap
return gap
def get_bulk_green_function(h0, energy=0.0, eta=1e-3):
"""Function to compute the bulk Green's function"""
from pygra import geometry
from pygra import green
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian()
h.intra = np.matrix(h0.intra)
h.tx = np.matrix(h0.tx)
h.ty = np.matrix(h0.ty)
h.txy = np.matrix(h0.txy)
h.txmy = np.matrix(h0.txmy)
h.is_multicell
#gf,selfe = green.bloch_selfenergy(h,energy=energy,delta=eta,mode="full",nk=10)
# gf,selfe = green.bloch_selfenergy(h,energy=energy,delta=eta,mode="renormalization")
gf, selfe = green.bloch_selfenergy(h,
energy=energy,
delta=eta,
mode="adaptive")
return gf # return Green's function
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.environ['PYGRAROOT'])
import numpy as np
from pygra import geometry
import os
from pygra import groundstate
from pygra.selfconsistency import densitydensity
g = geometry.honeycomb_lattice(3)
h = g.get_hamiltonian(has_spin=False) # create hamiltonian of the system
nk = 3
filling = 0.5
g = 2.0 # interaction
V1s = np.linspace(0., 3.0, 10)
V2s = np.linspace(0., 3.0, 10)
#scf = scftypes.selfconsistency(h,nk=nk,filling=filling,g=g,mode="V")
def get_gap(V1, V2):
os.system("rm -f MF.pkl")
scf = densitydensity.Vinteraction(h, V1=V1, V2=V2, nk=nk, filling=filling)
return scf.hamiltonian.get_gap() # get the Hamiltonian
f = open("MAP.OUT", "w")
for V1 in V1s:
# 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.chain()
g = geometry.honeycomb_lattice()
#g = geometry.kagome_lattice()
g = g.supercell(3)
h = g.get_hamiltonian() # create hamiltonian of the system
h = h.get_multicell()
h.remove_spin()
mf = np.random.random(h.intra.shape) -.5
mf = np.matrix(mf)
mf = mf + mf.H
scf = scftypes.selfconsistency(h,nkp=1,filling=0.5,g=3.0,
mix=0.9,mf=mf,mode="V")
h = scf.hamiltonian # get the Hamiltonian
h.get_bands() # calculate band structure
from pygra import groundstate
groundstate.hopping(h,nrep=3) # write three replicas
#spectrum.fermi_surface(h)
# 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 topology import numpy as np from pygra import phasediagram g = geometry.honeycomb_lattice() # create geometry of a chain def getz2(x1,x2): # calculate the Z2 invariant for certain Zeeman and Rashba h = g.get_hamiltonian(has_spin=True) # get the Hamiltonian, spinfull h.add_kane_mele(x1) # add SOC h.add_sublattice_imbalance(x2) # add mass z2 = topology.z2_invariant(h,nk=10,nt=10) # get the Z2 print(x1,x2,z2) return z2 # now write the Phase diagram in a file phasediagram.diagram2d(getz2,x=np.linspace(-.05,0.05,10,endpoint=True),y=np.linspace(-.1,.1,10,endpoint=True),nite=3)
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src")
# 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() # create a honeycomb lattice
h0 = g.get_hamiltonian() # create hamiltonian of the system
h0.add_kane_mele(0.05) # Add Kane-Mele SOC
ps = np.linspace(0., 1., 30) # create different angles, from 0 to pi
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
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src")
import numpy as np
from pygra import geometry
g = geometry.honeycomb_lattice() # geometry of a honeycomb lattice
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
h.shift_fermi(3.0) # bottom of the band
h.add_rashba(0.5) # add Rashba SOC
h.add_zeeman([0., 0., 0.5]) # add a Zeeman field
h.add_swave(0.1) # add s-wave superconductivity
c = h.get_chern(nk=20) # compute Chern number
print()
print("########################")
print("Chern number = ", round(c, 2))
print("########################")
print()
h.get_bands(operator="sx") # compute band structure
# 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() # create a honeycomb lattice
h0 = g.get_hamiltonian() # create hamiltonian of the system
ps = np.linspace(0.,.1,5) # create the different KM couplings
es0 = [] # empty list for the total energies
es1 = [] # 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
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
# 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 geometry
from pygra import scftypes
import numpy as np
# create the hamiltonian
g = geometry.honeycomb_lattice() # triangular lattice geometry
#g = geometry.chain()
#g = g.supercell(2)
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
q = [1./3.,1./3.,0.]
q = [0.,0.,0.]
q = np.array(q) + 0.05
vector = [0.,0.,1.]
h.generate_spin_spiral(vector=[0.,0.,1.],qspiral=q,
fractional=True)
h.add_zeeman([.0,0.2,0.0])
#h.add_zeeman([[.0,0.1,0.0],[0.,-0.1,0.]])
h.get_bands(operator="sz")
