def K2inv_mat22(E,L,a2):
nklist = defns.list_nnk(E,L)
K2inv22 = []
for nkvec in nklist:
kvec = [i*2*pi/L for i in nkvec]
K2inv22.append(K2inv(E,kvec,2,0,0,0,0,a2)*np.identity(5))
return block_diag(*K2inv22)
def P_irrep_subspace_22(E, L, I):
N = len(defns.list_nnk(E, L))
Psub = np.zeros((5 * N, 0))
for shell in defns.shell_list(E, L):
Psub = np.column_stack(
(Psub, P_irrep_subspace_o_l(E, L, I, shell, 2, lblock=True)))
return Psub
def K33Bmat(E, L, a0, a2):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
#print(nnk_list)
#print(N)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((6, 6))
for i1 in range(6):
[l1, m1] = Gmatrix.lm_idx(i1)
for i2 in range(6):
[l2, m2] = Gmatrix.lm_idx(i2)
Gpk[i1,
i2] = K33B.K3cubicB(E, 2 * math.pi / L * np.array(nnp),
l1, m1,
2 * math.pi / L * np.array(nnk),
l2, m2)
Gp.append(Gpk)
Gfull.append(Gp)
matrix = np.ones_like(chop(np.block(Gfull)))
print(matrix.shape)
return pr.irrep_proj(matrix, E, L, "A1")
def Xi00(e, L):
nklist = list_nnk(e, L)
res = []
for nnk in nklist:
res.append(1. / ktinvroot(e, L, sums.norm(nnk)))
return np.diag(res)
def K2inv_mat00(E,L,a0,r0,P0):
nklist = defns.list_nnk(E,L)
K2inv00 = []
for nkvec in nklist:
kvec = [i*2*pi/L for i in nkvec]
K2inv00.append(K2inv(E,kvec,0,0,a0,r0,P0,0))
return np.diag(K2inv00)
def Gmat(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
#print(nnk_list)
#print(N)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((6, 6))
for i1 in range(6):
[l1, m1] = lm_idx(i1)
for i2 in range(6):
[l2, m2] = lm_idx(i2)
Gpk[i1, i2] = G(E, L, nnp, nnk, l1, m1, l2, m2)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
def K3mat(E, L, K0, K1, K2, A, B, Ytype):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
K3full = []
for p in range(N):
pvec = [i * 2 * pi / L for i in nnk_list[p]]
K3p = []
for k in range(N):
kvec = [i * 2 * pi / L for i in nnk_list[k]]
K3pk = np.zeros((6, 6))
for i1 in range(6):
[lp, mp] = lm_idx(i1)
for i2 in range(6):
[l, m] = lm_idx(i2)
K3pk[i1][i2] = K3quad(E, pvec, lp, mp, kvec, l, m, K0, K1,
K2, A, B, Ytype)
K3p.append(K3pk)
K3full.append(K3p)
return chop(np.block(K3full))
def K3mat_old(E, L, K0, K1, K2, A, B, Ytype):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
K3_00 = np.zeros((N, N))
K3_02 = np.zeros((N, 5 * N))
K3_20 = np.zeros((5 * N, N))
K3_22 = np.zeros((5 * N, 5 * N))
for i in range(N):
pvec = [npi * 2 * pi / L for npi in nnk_list[i]]
for j in range(N):
kvec = [nki * 2 * pi / L for nki in nnk_list[j]]
K3_00[i][j] = K3quad(E, pvec, 0, 0, kvec, 0, 0, K0, K1, K2, A, B,
Ytype)
for mp in range(-2, 3):
I = (mp + 2) * N + i
K3_20[I][j] = K3quad(E, pvec, 2, mp, kvec, 0, 0, K0, K1, K2, A,
B, Ytype)
for m in range(-2, 3):
J = (m + 2) * N + j
K3_22[I][J] = K3quad(E, pvec, 2, mp, kvec, 2, m, K0, K1,
K2, A, B, Ytype)
if mp == 2: # only do this once (mp==2 is arbitrary)
K3_02[i][J] = K3quad(E, pvec, 0, 0, kvec, 2, m, K0, K1,
K2, A, B, Ytype)
return full_matrix(K3_00, K3_20, K3_02, K3_22)
def RHO00(e, L):
nklist = list_nnk(e, L)
res = []
for nnk in nklist:
res.append(rho1mH(e, L, sums.norm(nnk)))
return np.diag(res)
def RHO22(e, L):
nklist = list_nnk(e, L)
res = []
for i in range(5):
for nnk in nklist:
res.append(rho1mH(e, L, sums.norm(nnk)))
return np.diag(res)
def F2_22_matrix(e, L, m1, m2):
alpha = 0.5
nklist = list_nnk(e, L)
F2_22 = []
for nnk in nklist:
#print(nnk)
res = sums.F2KSS(e, L, nnk, 2, m1, 2, m2, alpha)
F2_22.append(res)
return np.diag(F2_22)
def F2_20_matrix(e, L, m):
nklist = list_nnk(e, L)
alpha = 0.5
F2_20 = []
for nnk in nklist:
res = sums.F2KSS(e, L, nnk, 2, m, 0, 0, alpha)
F2_20.append(res)
return np.diag(F2_20)
def F2_02_matrix(e, L, m):
nklist = list_nnk(e, L)
alpha = 0.5
F2_02 = []
for nnk in nklist:
# print(nnk)
res = sums.F2KSS(e, L, nnk, 0, 0, 2, m, alpha)
F2_02.append(res)
return np.diag(F2_02)
def Gmat00(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = np.zeros((N, N))
for p in range(N):
nnp = list(nnk_list[p])
for k in range(N):
nnk = list(nnk_list[k])
Gfull[p][k] = G(E, L, nnp, nnk, 0, 0, 0, 0)
return chop(Gfull)
def p_iso00(E, L):
# No normalization
p_iso = np.ones((len(defns.list_nnk(E, L)), 1))
# Steve's convention: each column corresponds to a shell with 1/sqrt(N) normalization (so each vector has length=1)
# shells = defns.shell_list(E,L)
# p_iso = np.zeros((len(defns.list_nnk(E,L)),len(shells)))
# i_k = 0
# for i_shell in range(len(shells)):
# N = len(defns.shell_nnk_list(shells[i_shell]))
# p_iso[i_k:i_k+N,i_shell] = 1/sqrt(N)
# i_k += N
return p_iso
def full_F2_00_matrix(e, L):
alpha = 0.5
nklist = list_nnk(e, L)
F2_00 = []
for nnk in nklist:
res = sums.F2KSS(e, L, nnk, 0, 0, 0, 0, alpha)
F2_00.append(res)
return np.diag(F2_00)
def A22(e, L, a2):
nklist = list_nnk(e, L)
# q = np.sqrt(1-sums.E2a2(e,k))
# nklist = list_nnk(e,L)
# matrixa = np.diag(np.ones(len(nklist)*5)*(-1/(a2**5*q**4)))
res = []
for i in range(5):
for nnk in nklist:
q4 = (1 - sums.E2a2(e, 2 * math.pi * sums.norm(nnk) / L))**4
res.append(-1 / (a2**5 * q4))
# print(res)
return np.diag(res)
def G00(e, L):
nklist = list_nnk(e, L)
G_00 = np.zeros((len(nklist), len(nklist)))
#G_00 = np.zeros((len(nklist),len(nklist)),dtype=complex)
i = 0
for nnp in nklist: # TB: I reversed nnp and nnk
j = 0
for nnk in nklist:
# print(nnk, nnp)
G_00[i][j] = G(e, L, nnp, nnk, 0, 0, 0, 0)
j += 1
i += 1
return G_00
def G22m(e, L, m1, m2):
nklist = list_nnk(e, L)
G_22 = np.zeros((len(nklist), len(nklist)))
#G_22 = np.zeros((len(nklist),len(nklist)),dtype=complex)
i = 0
for nnp in nklist: # TB: I reversed nnp and nnk
j = 0
for nnk in nklist:
# print(nnk, nnp)
G_22[i][j] = G(e, L, nnp, nnk, 2, m1, 2, m2)
j += 1
i += 1
return G_22
def Gmat00(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
# print(nnk_list)
# print(list(nnk_list[0]))
Gfull = np.zeros((N, N))
for p in range(N):
# nnp = list(nnk_list[p])
nnp = nnk_list[p]
for k in range(N):
# nnk = list(nnk_list[k])
nnk = nnk_list[k]
Gfull[p, k] = G(E, L, np.array(nnp), np.array(nnk), 0, 0, 0, 0)
return chop(Gfull)
def K2inv_mat(E,L,a0,r0,P0,a2):
nnk_list = defns.list_nnk(E,L)
N = len(nnk_list)
K2i_full = []
for k in range(N):
kvec = [ ki*2*pi/L for ki in nnk_list[k] ]
K2i_k_diag = []
for i in range(6):
[l,m] = defns.lm_idx(i)
K2i_k_diag.append(K2inv(E,kvec,l,m,a0,r0,P0,a2))
K2i_k = np.diag(K2i_k_diag)
K2i_full.append(K2i_k)
return block_diag(*K2i_full)
def P_irrep_subspace(E, L, I):
# P_I = P_irrep_full(E,L,I)
# elist, vlist = LA.eig(P_I)
# # eigenvalues should all be 0 or 1; only want 1's
# ivec = [i for i,e in enumerate(elist) if abs(e-1)<1e-13]
# if len(ivec) != int(round(np.trace(P_I))):
# print('Error in P_irrep_subspace: wrong subspace dimension')
# Psub = defns.chop(vlist[:,ivec].real)
# if Psub.shape[1]==0:
# return Psub
# else:
# return defns.chop(LA.qr(Psub)[0]) # orthonormalize
N = len(defns.list_nnk(E, L))
Psub = np.zeros((6 * N, 0))
for shell in defns.shell_list(E, L):
Psub = np.column_stack((Psub, P_irrep_subspace_o(E, L, I, shell)))
return Psub
def K2inv_mat2(E, L, a2):
nklist = defns.list_nnk(E, L)
K2inv2 = []
for nkvec in nklist:
kvec = [i * 2 * pi / L for i in nkvec]
K2inv2.append(K2inv(E, kvec, 2, 0, 0, 0, 0, a2))
# Potentially faster method (pre-allocates memory)
# blocksize = len(nklist)
# K2inv2 = [None]*blocksize
# for i in range(0,blocksize):
# kvec = [j*2*pi/L for j in nklist[i]]
# K2inv2[i] = K2inv(E,kvec,2,0,0,0,0,a2)
K2_block = np.diag(K2inv2)
return np.kron(np.identity(5), K2_block)
def Gmat22(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((5, 5))
for mp in range(-2, 3):
for m in range(-2, 3):
Gpk[mp, m] = G(E, L, nnp, nnk, 2, mp, 2, m)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
def Gmat22(E, L):
nnk_list = list_nnk(E, L)
N = len(nnk_list)
Gfull = []
for p in range(N):
nnp = list(nnk_list[p])
Gp = []
for k in range(N):
nnk = list(nnk_list[k])
Gpk = np.zeros((5, 5))
for i in range(5):
for j in range(5):
mp = i - 2
m = j - 2
Gpk[i, j] = G(E, L, nnp, nnk, 2, mp, 2, m)
Gp.append(Gpk)
Gfull.append(Gp)
return chop(np.block(Gfull))
npsqrt = np.sqrt
exp = np.exp
def getnmax(cutoff,alpha,x2,gamma):
eqn = lambda l : -cutoff + 2*math.pi*npsqrt(math.pi/alpha) * exp(alpha*x2)*erfc(npsqrt(alpha)*l)
n0=1
solution=fsolve(eqn, n0)
print(max(solution*gamma,1)+3)
return int(np.round(max(solution*gamma,1)+3))
L=84
E=2.9972794820231976
print(len(defns.list_nnk(E,L)))
exit()
a0=25
r0=8.34
E=3.1
L=10
k=2.25
IPV=-1
print(K2.K2inv(E,np.array([0.,0.,k*2*math.pi/L]),0,0,a0,r0,0.,0.,IPV))
exit()
def A00(e, L, a):
nklist = list_nnk(e, L)
matrixa = np.diag(np.ones(len(nklist)) * (-1 / a))
return matrixa
