mirror of
https://github.com/triqs/dft_tools
synced 2024-12-26 06:14:14 +01:00
196 lines
9.6 KiB
Python
196 lines
9.6 KiB
Python
|
|
################################################################################
|
|
#
|
|
# TRIQS: a Toolbox for Research in Interacting Quantum Systems
|
|
#
|
|
# Copyright (C) 2011 by M. Ferrero, O. Parcollet
|
|
#
|
|
# TRIQS is free software: you can redistribute it and/or modify it under the
|
|
# terms of the GNU General Public License as published by the Free Software
|
|
# Foundation, either version 3 of the License, or (at your option) any later
|
|
# version.
|
|
#
|
|
# TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
|
|
# WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
|
|
# FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
|
|
# details.
|
|
#
|
|
# You should have received a copy of the GNU General Public License along with
|
|
# TRIQS. If not, see <http://www.gnu.org/licenses/>.
|
|
#
|
|
################################################################################
|
|
|
|
import numpy
|
|
from tight_binding import TBLattice
|
|
|
|
__all__ = ['TBSuperLattice']
|
|
|
|
|
|
def nint_strict(x, precision=1.e-9):
|
|
""" Round array x to the closest integer and asserts that its distance to this integer is less than precision.
|
|
precision must satisfy : precision >0 and precision <0.5
|
|
"""
|
|
assert precision >0 and precision <0.5, "nint_strict : precision makes no sense !"
|
|
i = numpy.floor(x+0.5)
|
|
assert abs(i-x).max() < precision, repr(i) + "\n "+repr(x) + "\n The Float is not close enough to the integer "
|
|
return i.astype(numpy.int)
|
|
|
|
|
|
class TBSuperLattice(TBLattice):
|
|
"""
|
|
Builds a superlattice on top of a base Lattice, by picking superlattice units and optionally the cluster points.
|
|
"""
|
|
def __init__(self, tb_lattice, super_lattice_units, cluster_sites = None, remove_internal_hoppings = False):
|
|
"""
|
|
* tb_lattice: The underlying lattice
|
|
|
|
* super_lattice_units: The unit vectors of the superlattice in the tb_lattice (integer) coordinates
|
|
|
|
* cluster_sites [None]: Coordinates of the cluster in tb_lattice coordinates.
|
|
If None, an automatic computation of cluster positions is made as follows:
|
|
it takes all points whose coordinates in the basis of the superlattice are in [0, 1[^dimension
|
|
|
|
* remove_internal_hoppings: If true, the hopping terms are removed inside the cluster.
|
|
Useful to add Hartree Fock terms at the boundary of a cluster, e.g.
|
|
"""
|
|
if not isinstance(tb_lattice, TBLattice): raise ValueError, "tb_lattice should be an instance of TBLattice"
|
|
self.__BaseLattice = tb_lattice
|
|
dim = tb_lattice.dim
|
|
|
|
try:
|
|
self.__super_lattice_units = numpy.array(super_lattice_units, copy=True)
|
|
assert self.__super_lattice_units.shape == (dim, dim)
|
|
except:
|
|
raise ValueError, "super_lattice_units is not correct. Cf Doc. value is %s, dim = %s "%(super_lattice_units,dim)
|
|
|
|
Ncluster_sites = int(numpy.rint(abs(numpy.linalg.det(self.__super_lattice_units ))))
|
|
assert Ncluster_sites >0, "Superlattice vectors are not independant !"
|
|
self._M = self.__super_lattice_units.transpose()
|
|
self._Mtilde = numpy.array(numpy.rint(numpy.linalg.inv(self._M)*Ncluster_sites), dtype = int)
|
|
|
|
self.__remove_internal_hoppings = remove_internal_hoppings
|
|
#self.norb = tb_lattice.NOrbitalsInUnitCell
|
|
self.Norb = tb_lattice.NOrbitalsInUnitCell * Ncluster_sites
|
|
|
|
# cluster_sites computation
|
|
if cluster_sites!=None:
|
|
self.__cluster_sites = list(cluster_sites)[:]
|
|
else: # Computes the position of the cluster automatically
|
|
self.__cluster_sites = []
|
|
#We tile the super-cell with the tb_lattice points and retains
|
|
# the points inside it and store it.
|
|
M=numpy.array(self.__super_lattice_units)
|
|
assert M.shape==tuple(2*[dim]), "Tiling Construct: super_lattice_units does not have the correct size"
|
|
#Minv = Ncluster_sites*numpy.linalg.inverse(M) #+0.5 # +0.5 is for the round
|
|
#Mtilde = Minv.astype(numpy.Int) # now is integer.
|
|
Mtilde = nint_strict(Ncluster_sites*numpy.linalg.inv(M))
|
|
# round to the closest integer, with assert that precision is <1.e-9
|
|
if dim==1: a=(max(M[0,:]), 0, 0 )
|
|
elif dim==2: a=(2*max(M[0,:]), 2*max(M[1,:]), 0 )
|
|
elif dim==3: a= (3*max(M[0,:]), 3*max(M[1,:]), 3*max(M[2,:]))
|
|
else: raise ValueError, "dim is not between 1 and 3 !!"
|
|
r = lambda i: range(-a[i] , a[i]+1)
|
|
for nx in r(0):
|
|
for ny in r(1):
|
|
for nz in r(2):
|
|
nv = numpy.array([nx, ny, nz][0:dim])
|
|
k_sl = numpy.dot(Mtilde, nv)
|
|
if (min(k_sl) >= 0) and (max(k_sl) < Ncluster_sites ): # The point is a point of the cluster. We store it.
|
|
self.__cluster_sites.append(nv.tolist())
|
|
|
|
assert len(self.__cluster_sites) == Ncluster_sites, """Number of cluster positions incorrect (compared to the volume of unit cell of the Superlattice)"""
|
|
self.Ncluster_sites = Ncluster_sites
|
|
|
|
# creating a dictionnary position_of_sites -> number e.g. (1, 0): 2 etc...
|
|
# self._clustersites_hash = dict ([ (tuple(pos), n) for n, pos in enumerate(self.cluster_sites)])
|
|
|
|
# Compute the new Hopping in the supercell
|
|
Hopping = self.fold(tb_lattice.hopping_dict(), remove_internal_hoppings)
|
|
if 0:
|
|
for k, v in Hopping.items():
|
|
print k
|
|
print v.real
|
|
|
|
# Compute the new units of the lattice in real coordinates
|
|
Units = numpy.dot(self.__super_lattice_units, tb_lattice.Units)
|
|
|
|
# Positions and names of orbitals in the supercell: just translate all orbitals for cluster site positions
|
|
# in R^3 coordinates.
|
|
Orbital_Positions = [POS + tb_lattice.latt_to_real_x(CS) for POS in tb_lattice.OrbitalPositions for CS in self.__cluster_sites]
|
|
|
|
#Orbital_Names = [ '%s%s'%(n, s) for n in tb_lattice.OrbitalNames for s in range(Ncluster_sites)]
|
|
site_index_list, orbital_index_list = range(1, Ncluster_sites+1), tb_lattice.OrbitalNames
|
|
if len(orbital_index_list)==1:
|
|
Orbital_Names= [ s for s in site_index_list ]
|
|
elif len(site_index_list)==1 and len(orbital_index_list)>1:
|
|
Orbital_Names= [ o for o in orbital_index_list]
|
|
elif len(site_index_list)>1 and len(orbital_index_list)>1:
|
|
Orbital_Names= [ (pos, o) for o in orbital_index_list for pos in site_index_list]
|
|
|
|
#print tb_lattice.OrbitalNames #Orbital_Names
|
|
TBLattice.__init__(self, Units, Hopping, Orbital_Positions, Orbital_Names)
|
|
# we pass False since the folding has arealdy been done in tb_lattice
|
|
|
|
assert self.Norb == self.NOrbitalsInUnitCell
|
|
|
|
__HDF_reduction__ = ['__BaseLattice', '__super_lattice_units', '__cluster_sites', '__remove_internal_hoppings']
|
|
|
|
def __reduce__ (self):
|
|
return tuple([getattr(self, x) for x in self.__HDF_reduction__])
|
|
|
|
def fold(self, D1, remove_internal=False, create_zero = None):
|
|
""" Input: a function r-> f(r) on the tb_lattice given as a dictionnary
|
|
Output: the function R-> F(R) folded on the superlattice.
|
|
Only requirement is that f(r)[orbital1, orbital2] is properly defined.
|
|
Hence f(r) can be a numpy, a GFBloc, etc...
|
|
"""
|
|
#Res , norb = {} , self.__BaseLattice.NOrbitalsInUnitCell
|
|
Res , norb = {} , len(D1.values()[0])
|
|
pack = self.pack_index_site_orbital
|
|
for nsite, CS in enumerate(self.__cluster_sites):
|
|
for disp, t in D1.items():
|
|
R, alpha = self.change_coordinates_L_to_SL(numpy.array(CS)+numpy.array(disp))
|
|
if R not in Res: Res[R] = create_zero() if create_zero else numpy.zeros((self.Norb, self.Norb), dtype = type(t[0,0]))
|
|
if not(remove_internal) or R!= self.tb_lattice.dim*(0, ):
|
|
for orb1 in range(norb):
|
|
for orb2 in range(norb):
|
|
Res[R][pack(nsite, orb1), pack(alpha, orb2)] += t[orb1, orb2]
|
|
return Res
|
|
|
|
def change_coordinates_SL_to_L(self, R , alpha):
|
|
"""Given a point in the supercell R, site (number) alpha, it computes its position on the tb_lattice in lattice coordinates"""
|
|
return numpy.dot (self._M, numpy.array(R)) + self.__cluster_sites[alpha,:]
|
|
|
|
def change_coordinates_L_to_SL(self, x):
|
|
"""Given a point on the tb_lattice in lattice coordinates, returns its coordinates (R, alpha) in the Superlattice"""
|
|
aux = numpy.dot(self._Mtilde, numpy.array(x))
|
|
R = aux // self.Ncluster_sites
|
|
dx = list (x - numpy.dot (self._M, R) ) # force int ?
|
|
return tuple(R), self.__cluster_sites.index(dx)
|
|
|
|
def pack_index_site_orbital(self, n_site, n_orbital):
|
|
""" nsite and n_orbital must start at 0"""
|
|
return n_site + (n_orbital ) * self.Ncluster_sites
|
|
|
|
def unpack_index_site_orbital (self, index):
|
|
"""Inverse of pack_index_site_orbital"""
|
|
n_orbital = (index)//self.Ncluster_sites
|
|
n_site = index - n_orbital*self.Ncluster_sites
|
|
return n_site, n_orbital
|
|
|
|
def cluster_sites(self):
|
|
"""
|
|
Generate the position of the cluster site in the tb_lattice coordinates.
|
|
"""
|
|
for pos in self.__cluster_sites:
|
|
yield pos
|
|
|
|
def __repr__(self):
|
|
def f(A):
|
|
return list([ tuple(x) for x in A])
|
|
return """SuperLattice class: \n
|
|
Base TBLattice: %s
|
|
SuperLattice Units: %s
|
|
Remove internal Hoppings: %s
|
|
Cluster site positions: %s"""%(self.__BaseLattice, f(self.__super_lattice_units), self.__cluster_sites, self.__remove_internal_hoppings)
|