Symmetry projection operator generation

Former-commit-id: 58b0d7b3f2a292c26964571edf159b26f0eef0ed
This commit is contained in:
Marek Nečada 2018-12-17 16:46:51 +02:00
parent a5739c6e74
commit 7bf6d1dc7b
1 changed files with 73 additions and 1 deletions

View File

@ -64,6 +64,10 @@ class SVWFPointGroupInfo: # only for point groups, coz in svwf_rep() I use I_tyt
def svwf_irrep_projectors(self, lMax, *rep_gen_func_args, **rep_gen_func_kwargs):
return gen_point_group_svwfrep_projectors(self.permgroup, self.irreps, self.svwf_rep(lMax, *rep_gen_func_args, **rep_gen_func_kwargs))
# alternative, for comparison and testing; should give the same results
def svwf_irrep_projectors2(self, lMax, *rep_gen_func_args, **rep_gen_func_kwargs):
return gen_point_group_svwfrep_projectors(self.permgroup, self.irreps, self.svwf_rep(lMax, *rep_gen_func_args, **rep_gen_func_kwargs))
# srcgroup is expected to be PermutationGroup and srcgens of the TODO
# imcmp returns True if two elements of the image group are 'equal', otherwise False
def generate_grouprep(srcgroup, im_identity, srcgens, imgens, immultop = None, imcmp = None):
@ -96,7 +100,7 @@ def mmult_tyty(a, b):
def mmult_ptypty(a, b):
return(qpms.apply_ndmatrix_left(a, b, (-6,-5,-4)))
def gen_point_group_svwfrep_projectors(permgroup, matrix_irreps_dict, sphrep_full):
def gen_point_group_svwfrep_irreps(permgroup, matrix_irreps_dict, sphrep_full):
'''
Gives the projection operators $P_kl('\Gamma')$ from Dresselhaus (4.28)
for all irreps $\Gamma$ of D3h.;
@ -131,6 +135,74 @@ def gen_point_group_svwfrep_projectors(permgroup, matrix_irreps_dict, sphrep_ful
sphreps[repkey] = sphrep
return sphreps
def gen_point_group_svwfrep_projectors(permgroup, matrix_irreps_dict, sphrep_full):
'''
The same as gen_point_group_svwfrep_irreps, but summed over the kl diagonal, so
one gets single projector onto each irrep space and the arrays have indices
[t, y, t, y]
'''
summedprojs = dict()
for repi, W in gen_point_group_svwfrep_irreps(permgroup, matrix_irreps_dict, sphrep_full).items():
irrepd = W.shape[0]
if irrepd == 1:
mat = np.reshape(W, W.shape[-4:])
else:
mat = np.zeros(W.shape[-4:], dtype=complex) # TODO the result should be real — check!
for d in range(irrepd):
mat += W[d,d]
if not np.allclose(mat.imag, 0):
raise ValueError("The imaginary part of the resulting projector should be zero, damn!")
else:
summedprojs[repi] = mat.real
return summedprojs
def gen_point_group_svwfrep_projectors2(permgroup, matrix_irreps_dict, sphrep_full, do_bases = False):
'''
an approach as in gen_hexlattice_Kpoint_svwf_rep_projectors; for comparison and testing
'''
nelem = sphrep_full.values[0].shape[-1]
if (do_bases):
bases = dict()
projectors = dict()
for repi, W in gen_point_group_svwfrep_irreps(permgroup, matrix_irreps_dict, sphrep_full).items():
totalvecs = 0
tmplist = list()
for t in (0,1):
for y in range(nelem):
for ai in range(W.shape[0]):
for bi in range(W.shape[1]):
v = np.zeros((2, nelem))
v[t,y] = 1
v1 = np.tensordot(W[ai,bi], v, axes = ([-2,-1],[0,1]))
if not np.allclose(v1,0):
v1 = normalize(v1)
for v2 in tmplist:
dot = np.tensordot(v1.conjugate(),v2, axes=([-2,-1],[0,1]))
if not (np.allclose(dot,0)):
if not np.allclose(np.abs(dot),1):
raise ValueError('You have to fix this piece of code.')
break
else:
totalvecs += 1
tmplist.append(v1)
theprojectors = np.zeros((2,nelem, 2, nelem), dtype = float)
if do_bases:
thebasis = np.zeros((len(tmplist), 2, nelem), dtype=complex)
for i, v in enumerate(tmplist):
thebasis[i] = v
beses[repi] = thebasis
for v in tmplist:
theprojector += (v[:,:,ň,ň] * v.conjugate()[ň,ň,ň,:,:,:]).real
for x in [0, 1, -1, sqrt(.5), -sqrt(.5), .5, -.5]:
theprojector[np.isclose(theprojector,x)] = x
if do_bases:
return projectors, bases
else:
return projectors
# Group D3h; mostly legacy code (kept because of the the honeycomb lattice K-point code, whose generalised version not yet implemented)
# Note that the size argument of permutations is necessary, otherwise e.g. c*c and b*b would not be evaluated equal
# N.B. the weird elements as Permutation(N) it means identity permutation of size N+1.