def gutz_model_setup(u=0.0, nmesh=5000):
'''Set up calculations for semi-circular DOS with two-ghost orbitals.
'''
# semi-circular energy mesh
sc = special.semicirular()
e_list = sc.get_e_list_of_uniform_wt(nmesh=nmesh)
a = tb.AtomsTB("N", [(0, 0, 0)], cell=(1, 1, 1))
a.set_orbitals_spindeg(orbitals=[("p")])
# set up hk_list
hk_list = [np.array([ \
[e*1.e-0, 0, 0.j ],\
[0 , e, 0 ], \
[0 , 0, e*1.e-0]]) for e in e_list]
aTB = tb.TB(a, hk_list=hk_list)
# dummy k-point list
kps = e_list
num_k = len(kps)
kps_wt = 1.0 / num_k * np.ones((num_k))
if aTB.Atoms.spindeg:
kps_wt *= 2
num_e = 0.0
num_band_max = 3
# GPARAMBANDS.h5
h1e_list = [
np.zeros((num_band_max * 2, num_band_max * 2), dtype=np.complex)
]
ginput.save_gparambands(kps_wt, num_e, num_band_max, \
ensemble=1, h1e_list=h1e_list)
# GPARAM.h5
# self-energy structure
sigma = np.zeros((6, 6), dtype=int)
sigma[0::2, 0::2] = np.arange(1, 10).reshape((3, 3))
sigma[1::2, 1::2] = sigma[0::2, 0::2]
# Coulomb matrix
v2e = np.zeros((6, 6, 6, 6), dtype=np.complex)
v2e[2, 2, 2, 2] = v2e[2, 2, 3, 3] = v2e[3, 3, 2, 2] = v2e[3, 3, 3, 3] = u
vdc2_list = np.array([[0, 0, -u / 2, -u / 2, 0, 0]])
ginput.save_gparam(na2_list=[6],
iembeddiag=-3,
imix=0,
sigma_list=[sigma],
v2e_list=[v2e],
nval_top_list=[6],
vdc2_list=vdc2_list)
# BAREHAM_0.h5
aTB.save_bareham(kps)
def gutz_model_setup(u=0.0, nmesh=5000, norb=1, tiny=0.0, mu=0):
'''Set up calculations for semi-circular DOS with two-ghost orbitals.
'''
# semi-circular energy mesh
sc = special.semicirular()
e_list = sc.get_e_list_of_uniform_wt(nmesh=nmesh)
a = tb.AtomsTB("N", [(0, 0, 0)], cell=(1, 1, 1))
a.set_orbitals_spindeg(orbitals=[tuple(["s" for i in range(norb)])])
# set up hk_list
hk_list = [get_hk1(e, tiny, norb) for e in e_list]
aTB = tb.TB(a, hk_list=hk_list)
# dummy k-point list
kps = e_list
num_k = len(kps)
kps_wt = 1.0 / num_k * np.ones((num_k))
if aTB.Atoms.spindeg:
kps_wt *= 2
num_e = 0.0
norb2 = norb * 2
# GPARAMBANDS.h5
h1e_list = [np.zeros((norb2, norb2), dtype=np.complex)]
ginput.save_gparambands(kps_wt, num_e, norb, \
ensemble=1, h1e_list=h1e_list)
# GPARAM.h5
# self-energy structure
sigma = np.zeros((norb2, norb2), dtype=int)
sigma[0::2, 0::2] = np.arange(1,norb**2+1).reshape( \
(norb,norb))
sigma[1::2, 1::2] = sigma[0::2, 0::2]
# Coulomb matrix
v2e = np.zeros((norb2, norb2, norb2, norb2), dtype=np.complex)
v2e[0, 0, 0, 0] = v2e[0, 0, 1, 1] = v2e[1, 1, 0, 0] = v2e[1, 1, 1, 1] = u
vdc2_list = np.array([np.zeros((norb2))])
vdc2_list[0, 0:2] = -u / 2 + mu
ginput.save_gparam(na2_list=[norb2],
iembeddiag=-3,
imix=0,
sigma_list=[sigma],
v2e_list=[v2e],
nval_top_list=[norb2],
vdc2_list=vdc2_list,
max_iter=5000)
# BAREHAM_0.h5
aTB.save_bareham(kps)
def gutz_model_setup(u=0.0, spindeg=True, num_e=2., iembeddiag=-1):
'''Set up Gutzwiller calculations for 2d body-centered square lattice.
Parameters:
* u: real number
Hubbard U.
* spindeg: boolean number
whether to keep spin degeneracy or not.
* num_e: real number
number of electron per unit cell
* iembeddiag: integer
flag for method to solve the embedding Hamiltonian.
* -3: valence truncation ED with S=0 (spin-singlet) constraint;
* -1: valence truncation ED;
* 10: Hartree-Fock.
Result:
Create all the necessary input file of ``GPARAMBANDS.h5``, ``GPARAM.h5``,
and ``BAREHAM_0.h5``, for *CyGutz* calculation.
'''
# two "H" atoms in the square unit cell, one at the corner
# and one at the center.
symbols = ['H', 'H']
scaled_positions = [(0, 0, 0), (0.5, 0.5, 0)]
cell = np.identity(3)
a = tb.AtomsTB(symbols=symbols,
scaled_positions=scaled_positions,
cell=cell)
# set spin degeneracy accordingly.
a.set_orbitals_spindeg(spindeg=spindeg)
# create a tight-binding model class given the AtomsTB.
aTB = tb.TB(a)
# set real space (nearest neighbour) hopping elements.
t = -1.0
aTB.set_hop([
((0, 0, 0), 0, 1, t),
((-1, 0, 0), 0, 1, t),
((0, -1, 0), 0, 1, t),
((-1, -1, 0), 0, 1, t),
((0, 0, 0), 1, 0, t),
((1, 0, 0), 1, 0, t),
((0, 1, 0), 1, 0, t),
((1, 1, 0), 1, 0, t),
])
# set 2d k-mesh
kps_size = (50, 50, 1)
kps = kpoints.monkhorst_pack(kps_size)
# set uniform k-point weight
num_k = len(kps)
kps_wt = 1.0 / num_k * np.ones((num_k))
if aTB.Atoms.spindeg:
kps_wt *= 2
# se maximal number of bands (here we have two bands.)
num_band_max = 2
# set list of one-body part of the local Hamiltonian (trivial here.)
h1e_list = [np.array([[
0,
]], dtype=np.complex) for symbol in symbols]
# create ``GPARAMBANDS.h5`` file
ginput.save_gparambands(kps_wt, num_e, num_band_max, h1e_list=h1e_list)
# cerate ``BAREHAM_0.h5`` file.
aTB.save_bareham(kps)
# for initializing CyGutz calculation
from pyglib.gutz.batch_init import batch_initialize
if spindeg:
spin_polarization = 'n'
else:
spin_polarization = 'y'
# the default settings are good for this model.
batch_initialize(cell=cell,
scaled_positions=scaled_positions,
symbols=symbols,
idx_equivalent_atoms=[0, 1],
unique_u_list_ev=[u],
iembeddiag=iembeddiag,
spin_polarization=spin_polarization,
updn_full_list=[1, -1])
# save the aTB
with open('aTB.pckl', 'wb') as f:
pickle.dump([a, aTB], f)
def gutz_model_setup(u=0.0, nmesh=5000, mu=0):
'''Set up Gutzwiller calculations for 1-band model with semi-circular DOS.
Parameters:
* u: real number
Hubbard U.
* nmesh: interger number
number of energy mesh
* mu: real number
chemical potential
Result:
Create all the necessary input file of ``GPARAMBANDS.h5``, ``GPARAM.h5``,
and ``BAREHAM_0.h5``, for *CyGutz* calculation.
'''
# get semi-circular class, predifined in pyglib.model.special
sc = special.semicircular()
# get semi-circular energy mesh
e_list = sc.get_e_list_of_uniform_wt(nmesh=nmesh)
# get atomic structure with 1 atom per unit cell.
a = tb.AtomsTB("N", [(0, 0, 0)], cell=(1, 1, 1))
# specify single s-orbital and orbital dimensions.
a.set_orbitals_spindeg(orbitals=[('s')])
norb = 1
norb2 = norb * 2
# get a list of one-body Hamilonian for the enrgy mesh.
hk_list = [np.array([[e + 0.j]]) for e in e_list]
# get the tight-binding model
aTB = tb.TB(a, hk_list=hk_list)
# here the energy mesh is the same as k-points.
kps = e_list
num_k = len(kps)
# set uniform k-point weight.
kps_wt = 1.0 / num_k * np.ones((num_k))
# Include the spin degeneracy to k-point weight.
if aTB.Atoms.spindeg:
kps_wt *= 2
# We will work with grand canonical model, num_e will not be used.
num_e = 0.0
# list of one-body part of the local Hamiltonians.
# here the s-orbital is located at zero.
h1e_list = [np.zeros((norb2, norb2), dtype=np.complex)]
# generate GPARAMBANDS.h5
# ensemble is set to 1 for grand canonical system.
ginput.save_gparambands(kps_wt, num_e, norb, \
ensemble=1, h1e_list=h1e_list, delta=1.e-8)
# set self-energy structure
sigma = np.zeros((norb2, norb2), dtype=int)
sigma[0::2, 0::2] = np.arange(1,norb**2+1).reshape( \
(norb,norb))
sigma[1::2, 1::2] = sigma[0::2, 0::2]
# set Coulomb matrix
v2e = np.zeros((norb2, norb2, norb2, norb2), dtype=np.complex)
v2e[0, 0, 0, 0] = v2e[0, 0, 1, 1] = v2e[1, 1, 0, 0] = v2e[1, 1, 1, 1] = u
# set the potential shift such that the system has particle-hole
# symmetry with recpect to zero.
# also include chemical potential here.
vdc2_list = np.array([np.zeros((norb2))])
vdc2_list[0, 0:2] = -u / 2 + mu
# generate GPARAM.h5 file.
ginput.save_gparam(na2_list=[norb2],
iembeddiag=-1,
imix=0,
sigma_list=[sigma],
v2e_list=[v2e],
nval_top_list=[norb2],
vdc2_list=vdc2_list,
max_iter=500)
# generate BAREHAM_0.h5 file.
aTB.save_bareham(kps)
((0, 0, 0), 0, 1, 0.25), ((0, 0, 0), 1, 0, 0.25)])
kps_size = (100, 1, 1)
kps = kpoints.monkhorst_pack(kps_size)
num_k = len(kps)
kps_wt = 1.0 / num_k * np.ones((num_k))
if aTB.Atoms.spindeg:
kps_wt *= 2
num_e = 1.2
num_band_max = 2
# GPARAMBANDS.h5
h1e_list = [np.array([[0,0,0.25,0],[0,0,0,0.25],[0.25,0,0,0],[0,0.25,0,0]], \
dtype=np.complex)]
ginput.save_gparambands(kps_wt, num_e, num_band_max, h1e_list=h1e_list)
# GPARAM.h5
sigma = np.zeros((4, 4), dtype=np.int32)
sigma[0::2, 0::2] = np.arange(1, 5).reshape((2, 2))
sigma[1::2, 1::2] = sigma[0::2, 0::2]
v2e = np.zeros((4, 4, 4, 4), dtype=np.complex)
v2e[0, 0, 0, 0] = v2e[0, 0, 1, 1] = v2e[1, 1, 0, 0] = v2e[1, 1, 1, 1] = 8.0
v2e[2:, 2:, 2:, 2:] = v2e[0:2, 0:2, 0:2, 0:2]
ryd2ev = s_const.physical_constants['Rydberg constant times hc in eV'][0]
sz = np.asarray(np.diag((1, -1, 1, -1)), dtype=np.complex)
ginput.save_gparam(na2_list=[4],
iembeddiag=-1,
imix=-1,
sigma_list=[sigma],
v2e_list=[v2e],