def get(U):
"""Perform a selfconsistent calculation"""
print(U)
h = g.get_hamiltonian() # create hamiltonian of the system
mf = meanfield.guess(h,mode="ferro") # ferro initialization
# perform SCF with specialized routine for Hubbard
fU = lambda r: U*fimpurity(r) # Hubbard for the site
scf = meanfield.Vinteraction(h,nk=20,
filling=0.5, # set at half filling
U=fU, # spatially dependent U
mix = 0.9, # quite agressive mixing
mf=mf, # initial guess
constrains=["no_charge"] # ignore chemical potential renorm
)
h = scf.hamiltonian # selfconsistent Hamiltonian
return h.compute_vev("sz")[0] # magnetization of the Hubbard site
def get():
h = g.get_hamiltonian() # create hamiltonian of the system
m = np.random.random(3) - 0.5
m = m / np.sqrt(m.dot(m)) # random magnetic field
h.add_zeeman(m)
nk = 30
filling = 0.25
h.turn_nambu()
mf = meanfield.guess(h, "random")
scf = meanfield.Vinteraction(h,
V1=-2.0,
nk=nk,
filling=filling,
mf=mf,
constrains=["no_charge"],
verbose=0)
h = scf.hamiltonian # get the Hamiltonian
h.check()
print(scf.identify_symmetry_breaking())
d = np.round(h.get_average_dvector(), 3)
print("d-vector", d, np.sum(d))
return h.get_gap()
# 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 meanfield
g = geometry.honeycomb_lattice()
g = g.supercell(1)
h = g.get_hamiltonian() # create hamiltonian of the system
U = 3.0
filling = 0.5
mf = meanfield.guess(h, mode="random")
scf = meanfield.Vinteraction(h,
nk=10,
U=U,
filling=filling,
mf=mf,
constrains=["no_charge"])
h = scf.hamiltonian # get the Hamiltonian
h.get_bands() # calculate band structure
# 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
from pygra import films
from pygra import meanfield
g = geometry.honeycomb_lattice()
g = g.supercell(3)
h = g.get_hamiltonian()
h.turn_nambu()
mf = meanfield.guess(h,"random")
scf = meanfield.Vinteraction(h,V1=-2.0,V2=-1.0,mf=mf,
nk=20,filling=0.5,mix=0.6,
compute_normal=True,
compute_dd=False,
compute_anomalous=True)
h = scf.hamiltonian
h.write_anomalous_hopping()
print(scf.identify_symmetry_breaking())
h.get_bands(operator="sz")
# 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 scipy.sparse import csc_matrix
from pygra import meanfield
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
h.add_swave(0.0)
U = -2.0
#hubbard = scftypes.hubbardscf
mf = meanfield.guess(h, mode="random")
scf = meanfield.Vinteraction(h,
nk=4,
U=U,
filling=0.7,
mf=mf,
compute_anomalous=True,
compute_dd=False)
h = scf.hamiltonian # get the Hamiltonian
h.get_bands(operator="electron") # calculate band structure
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src")
import numpy as np
from pygra import specialgeometry
from pygra.specialhopping import twisted_matrix
from pygra import meanfield
from pygra import groundstate
from pygra import geometry
g = specialgeometry.twisted_bilayer(4)
g = geometry.honeycomb_lattice()
g = g.supercell(3)
h = g.get_hamiltonian(is_sparse=True,
has_spin=False,
is_multicell=False,
mgenerator=twisted_matrix(ti=0.0, lambi=7.0))
mf = meanfield.guess(h, "dimerization")
scf = meanfield.Vinteraction(h,
nk=1,
filling=0.5,
V1=2.0,
V2=1.0,
mix=0.3,
mf=mf)
h = scf.hamiltonian # get the Hamiltonian
groundstate.hopping(
h, nrep=1, skip=lambda r1, r2: r1[2] * r2[2] < 0) # write three replicas
h.get_bands() # calculate band structure
h.write_onsite()
# Add the root path of the pygra library
import os
import sys
sys.path.append(os.environ['PYGRAROOT'])
from pygra import islands
import numpy as np
g = islands.get_geometry(name="honeycomb", n=3, nedges=3,
rot=0.0) # get an island
# maximum distance to the origin
h = g.get_hamiltonian(has_spin=True) # get the Hamiltonian
from pygra import meanfield
g.write()
mf = meanfield.guess(h, mode="ferro")
scf = meanfield.Vinteraction(h,
filling=0.5,
U=3.0,
V1=1.0,
mf=mf,
maxerror=1e-9)
scf.hamiltonian.write_hopping(spin_imbalance=True)
scf.hamiltonian.write_magnetization()
#scf.hamiltonian.get_bands()
from pygra import scftypes
from pygra import meanfield
import os
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
ds = []
Us = np.linspace(0.0, 10.0, 10)
h.add_swave(0.0)
os.system("rm -rf *.pkl")
U = 2.0
# SC and CDW guess
mf = 10 * (meanfield.guess(h, "swave") + meanfield.guess(h, "CDW"))
scf = meanfield.Vinteraction(
h,
nk=10,
mix=0.5,
U=-U,
mf=mf,
filling=0.45,
verbose=1,
V1=0.25, # first neighbor repulsion
# constrains=["no_charge"] # this forces the system to ignore CDW
# constrains=["no_SC"] # this forces the system to ignore SC
)
hscf = scf.hamiltonian
hscf.get_bands(operator="electron", nk=4000)
print("CDW order", np.abs(hscf.extract("CDW")))
print("SC order", np.abs(hscf.extract("swave")))
print("Gap", np.abs(hscf.get_gap()))
# 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
from pygra import meanfield
g = geometry.square_lattice() # square lattice
h = g.get_hamiltonian() # create hamiltonian of the system
h.add_swave(0.0) # activate a BdG Hamiltonian
mf = meanfield.guess(h, mode="random")
scf = meanfield.Vinteraction(
h,
nk=10, # number of k-points
U=-0.2, # interaction strength for the onsite interaction
filling=0.5, # filling of the system
mf=mf, # initial guess (ranodm should be ok)
mix=0.8, # mixing of the SCF
verbose=1, # this prints some info of the SCF
constrains=["no_normal_term"] # ignore normal terms of the SCF
)
h = scf.hamiltonian # get the selfconsistent Hamiltonian
print(scf.identify_symmetry_breaking())
h.get_bands(operator="electron") # calculate band structure
# 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 scipy.sparse import csc_matrix
from pygra import meanfield
g = geometry.honeycomb_lattice()
#g = geometry.kagome_lattice()
filling = 0.5
nk = 10
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
scf = meanfield.Vinteraction(h,
U=0.0,
V1=4.0,
nk=nk,
filling=filling,
mf="random")
from pygra import scftypes
print("Symmetry breaking", scf.identify_symmetry_breaking())
scf.hamiltonian.get_bands() # get the Hamiltonian
h = g.get_hamiltonian()
#h.add_kekule(.1)
#h.add_sublattice_imbalance(lambda r: 0.6*np.sign(r[2]))
h.add_antiferromagnetism(lambda r: 0.8 * np.sign(r[2]))
#h.add_antiferromagnetism(lambda r: 0.8*(r[2]>0))
#h.add_swave(lambda r: 0.8*(r[2]<0))
#h.add_swave(0.0)
mf = meanfield.guess(h, "kanemele")
#mf = meanfield.guess(h,"random")
h.add_kane_mele(0.01)
mf = None
scf = meanfield.Vinteraction(h,
V1=3.0,
U=0.0,
mf=mf,
V2=3.0,
V3=0.0,
nk=20,
filling=0.5,
mix=0.2,
compute_dd=False)
mix0 = h.extract("spin_mixing")
print("Mixing in original Hamiltonian", h.extract("spin_mixing"))
h = scf.hamiltonian
print("Mixing in new Hamiltonian", h.extract("spin_mixing"))
mix1 = h.extract("spin_mixing")
print("Enhancement of the spin mixing", mix1 / mix0)
#h.add_rashba(.1)
#h.add_antiferromagnetism(lambda r: 0.6*(r[2]>0))
#h.add_swave(lambda r: 0.6*(r[2]<0))
#print(h.extract("swave"))
print("Density", h.extract("density"))
# 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 scipy.sparse import csc_matrix from pygra import meanfield g = geometry.honeycomb_lattice() #g = geometry.kagome_lattice() g = g.supercell(1) filling = 0.5 nk = 10 h = g.get_hamiltonian(has_spin=False) # create hamiltonian of the system #scf = scftypes.selfconsistency(h,nk=nk,filling=filling,g=g,mode="V") scf = meanfield.Vinteraction(h, V2=1.0, nk=nk, filling=filling) from pygra import scftypes #scf = meanfield.hubbardscf(h,U=2.6,nk=nk,filling=filling) #scf = scftypes.hubbardscf(h,U=2.6,nk=nk,filling=filling) 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)
def faf(r):
return maf * np.sin(omega * np.pi * 2 * r[0])
h.add_antiferromagnetism(faf)
h.add_swave(fsc)
mf = meanfield.guess(h, "random")
mf = None
scf = meanfield.Vinteraction(h,
V1=1.0,
mf=mf,
filling=0.5,
mix=0.1,
compute_normal=True,
compute_dd=False,
compute_anomalous=True)
hscf = scf.hamiltonian
(inds, es) = h.get_bands()
(indsscf, esscf) = hscf.get_bands()
import matplotlib.pyplot as plt
plt.scatter(range(len(es)), es, c="red", label="Non-interacting")
plt.scatter(range(len(esscf)), esscf, c="blue", label="Interacting")
plt.legend()
sys.path.append(os.path.dirname(os.path.realpath(__file__)) + "/../../../src")
import numpy as np
from pygra import geometry
from pygra import meanfield
g = geometry.triangular_lattice() # square lattice
h = g.get_hamiltonian() # create hamiltonian of the system
h.add_zeeman([0., 0., 6.0]) # add exchange to promote triplet
h.add_swave(0.0) # activate a BdG Hamiltonian
mf = meanfield.guess(h, mode="random")
scf = meanfield.Vinteraction(h,
nk=20,
V1=-2.0,
filling=0.2,
mf=mf,
constrains=["no_normal_term"],
mix=0.8,
verbose=1)
hscf = scf.hamiltonian # SCF Hamiltonian
# now extract only the anomalous part
h0 = hscf.copy()
h0.remove_nambu() # remove SC (and Nambu as side effect)
h0.add_swave(0.0) # restore Nambu basis
print("SCF symmetry breaking", scf.identify_symmetry_breaking())
ha = hscf - h0 # this yields a Hamiltonian only with anomalous term
ha.get_bands() # band structure of only the anomalous term
# 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
from pygra import groundstate
from pygra import topology
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
nk = 10
filling = 0.5
from pygra import meanfield
#scf = scftypes.selfconsistency(h,nk=nk,filling=filling,g=g,mode="V")
h.add_zeeman([0.,0.,1.0])
mf = meanfield.guess(h,"dimerization")
mf = None
scf = meanfield.Vinteraction(h,V1=0.5,V2=0.5,nk=nk,filling=filling,
mf=mf,mix=0.2)
h = scf.hamiltonian # get the Hamiltonian
h.get_bands(operator="sz") # calculate band structure
groundstate.hopping(h)
topology.write_berry(h)
h.write_onsite()
# 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 scipy.sparse import csc_matrix
from pygra import meanfield
g = geometry.honeycomb_lattice()
h = g.get_hamiltonian() # create hamiltonian of the system
h.add_swave(0.0)
U = -2.0
#hubbard = scftypes.hubbardscf
mf = meanfield.guess(h,mode="random")
scf = meanfield.Vinteraction(h,nk=4,U=U,filling=0.7,mf=mf,
constrains = ["no_normal_term"])
h = scf.hamiltonian # get the Hamiltonian
print(scf.identify_symmetry_breaking())
h.get_bands(operator="electron") # calculate band structure
# 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 from pygra import groundstate from pygra import meanfield from scipy.sparse import csc_matrix g = geometry.chain() g = g.supercell(4) h = g.get_hamiltonian(has_spin=False) # create hamiltonian of the system nk = 10 filling = 0.5 mf = meanfield.guess(h, "dimerization") scf = meanfield.Vinteraction(h, V1=2.0, nk=nk, filling=filling, mf=mf) h = scf.hamiltonian # get the Hamiltonian h.get_bands() # calculate band structure from pygra import topology groundstate.hopping(h) print(np.round(h.intra, 3).real)
# We will take a ferromagnetic triangular lattice, whose
# superconducting state is a p-wave superfluid state with
# odd superconductivity
h.add_zeeman([0., 0., 20.0]) # add ferromagnetism
h.turn_nambu() # setup a Nambu hamiltonian
# the interaction terms are controlled by U, V1 and V2
# U is the onsite Hubbard interaction
# V1 is the first neighbor charge-charge interaction
# V2 is the second neighbor charge-charge interaction
mf = meanfield.guess(h, "random") # random intialization
scf = meanfield.Vinteraction(h,
U=0.0,
V1=-6.0,
V2=0.0,
nk=20,
filling=0.2,
mf=mf,
mix=0.3)
from pygra import scftypes
print("##########################################")
print("Symmetry breaking created by interactions")
print(scf.identify_symmetry_breaking())
print("##########################################")
# now extract the Hamiltonian and compute the bands
h = scf.hamiltonian # get the Hamiltonian
h.get_bands(operator="electron") # calculate band structure
# 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 scipy.sparse import csc_matrix
from pygra import meanfield
g = geometry.honeycomb_lattice()
nk = 10
h = g.get_hamiltonian(has_spin=True) # create hamiltonian of the system
filling = 0.7 # filling of the system
h.turn_nambu() # setup nambu degree of freedom
mf = meanfield.guess(h,"random")
scf = meanfield.Vinteraction(h,U=-3.0,V1=0.0,nk=nk,filling=filling,mf=mf,
verbose=1) # perform the SCF calculation
from pygra import scftypes
print("Symmetry breaking",scf.identify_symmetry_breaking())
scf.hamiltonian.get_bands(operator="electron",nk=2000) # get the Hamiltonian
def faf(r):
return maf * np.sin(omega * np.pi * 2 * r[0])
h.add_antiferromagnetism(faf)
h.add_swave(fsc)
mf = None
filling = 0.5
h.set_filling(filling)
mf = meanfield.guess(h, "random")
scf = meanfield.Vinteraction(h,
V1=-2.0,
mf=mf,
filling=filling,
mix=0.1,
verbose=1,
constrains=["no_normal_term"])
print(scf.identify_symmetry_breaking())
hscf = scf.hamiltonian
(inds, es) = h.get_bands()
(indsscf, esscf) = hscf.get_bands()
import matplotlib.pyplot as plt
plt.scatter(range(len(es)), es, c="red", label="Non-interacting")
plt.scatter(range(len(esscf)), esscf, c="blue", label="Interacting")
from pygra import films
from pygra import meanfield
g = geometry.diamond_lattice()
g = films.geometry_film(g, nz=4)
#g = g.supercell(3)
h = g.get_hamiltonian()
#h.add_antiferromagnetism(lambda r: 0.6*(r[2]>0))
#h.add_swave(lambda r: 0.6*(r[2]<0))
h.add_antiferromagnetism(lambda r: 0.8 * np.sign(r[2]))
#h.add_swave(lambda r: 0.2*r[2]>0.0)
#h.add_swave(0.0)
mf = meanfield.guess(h, "random")
#h.add_kane_mele(0.04)
#mf = None
scf = meanfield.Vinteraction(h,
V1=3.0,
U=0.0,
mf=mf,
V2=3.0,
V3=0.0,
nk=6,
filling=0.5,
mix=0.3,
compute_normal=True,
compute_dd=False,
compute_anomalous=False)
h = scf.hamiltonian
print(scf.identify_symmetry_breaking())
h.get_bands(operator="sz")
# 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 scipy.sparse import csc_matrix
from pygra import meanfield
g = geometry.honeycomb_lattice_C6()
g = geometry.honeycomb_lattice()
g = g.supercell(3)
filling = 0.5
nk = 10
h = g.get_hamiltonian(has_spin=False) # create hamiltonian of the system
#scf = scftypes.selfconsistency(h,nk=nk,filling=filling,g=g,mode="V")
mf = meanfield.guess(h,"dimerization")
scf = meanfield.Vinteraction(h,V1=4.0,mf=mf,
V2=2.0,nk=nk,filling=filling,mix=0.3)
h = scf.hamiltonian # get the Hamiltonian
h.get_bands() # calculate band structure
from pygra import groundstate
groundstate.hopping(h,nrep=3) # write three replicas
h.write_onsite(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.path.dirname(os.path.realpath(__file__))+"/../../../src")
import numpy as np
from pygra import geometry,meanfield
g = geometry.chain()
ns = 2 # make a supercell
g = g.supercell(ns)
h = g.get_hamiltonian() # create hamiltonian of the system
J = np.random.random(3) - 0.5 ; J = J/np.sqrt(J.dot(J)) # random vector
h.add_zeeman(J) # add magnetization in a random direction
h.setup_nambu_spinor() # tell the code to account for potential SC
scf = meanfield.Vinteraction(h,V1=-1.0,nk=10,filling=1./3.,mf="random",
verbose=1 # to print how the scf progresses
)
h = scf.hamiltonian # get the selfconssitent Hamiltonian
# write selfconsistent magnetization in MAGNETISM.OUT
scf.hamiltonian.write_magnetization(nrep=2)
# write non-unitarity of the d-vector in NON_UNITARITY_MAP.OUT
scf.hamiltonian.write_non_unitarity(nrep=2)
