def spacing_error(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = Hp_total.herm_conj()
Hz = 1 / 2 * com(Hp_total.sector.matrix(k), Hm.sector.matrix(k))
e, u = np.linalg.eigh(Hz)
psi = u[:, 0]
from Calculations import gen_fsa_basis, gram_schmidt
fsa_dim = int(pxp.N)
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(k), psi, fsa_dim)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
exp_vals = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(exp_vals, axis=0)):
exp_vals[n] = np.real(exp(Hz, fsa_basis[:, n]))
exp_diff = np.zeros(np.size(exp_vals) - 1)
for n in range(0, np.size(exp_diff, axis=0)):
exp_diff[n] = exp_vals[n + 1] - exp_vals[n]
M = np.zeros((np.size(exp_diff), np.size(exp_diff)))
for n in range(0, np.size(M, axis=0)):
for m in range(0, np.size(M, axis=1)):
M[n, m] = np.abs(exp_diff[n] - exp_diff[m])
error = np.power(np.trace(np.dot(M, np.conj(np.transpose(M)))), 0.5)
return error
def subspace_variance(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1, len(Hp)):
Hp_total = H_operations.add(Hp_total, Hp[n], np.array([1,
coef[n - 1]]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total, Hm, np.array([1, 1]))
H.sector.find_eig(k)
Hz = 1 / 2 * com(Hp_total.sector.matrix(k), Hm.sector.matrix(k))
e, u = np.linalg.eigh(Hz)
psi = u[:, 0]
from Calculations import gen_fsa_basis, gram_schmidt
fsa_dim = int(pxp.N)
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(k), psi, fsa_dim)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
H2 = np.dot(H.sector.matrix(k), H.sector.matrix(k))
H2_fsa = np.dot(np.conj(np.transpose(fsa_basis)), np.dot(H2, fsa_basis))
H_fsa = np.dot(np.conj(np.transpose(fsa_basis)),
np.dot(H.sector.matrix(k), fsa_basis))
subspace_variance = np.real(np.trace(H2_fsa - np.dot(H_fsa, H_fsa)))
return subspace_variance
def var_error(coef, pxp_config, pxxxp_config):
Hp = gen_Hp(pxp_config, pxxxp_config, coef)
Hm = np.conj(np.transpose(Hp))
H = Hp + Hm
Hz = 1 / 2 * com(Hp, Hm)
z = zm_state(2, 1, pxp, 1)
fsa_basis = gen_fsa_basis(Hp, z.prod_basis(), pxp.N)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
Hz_var = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_var, axis=0)):
Hz_var[n] = var(Hz, fsa_basis[:, n])
# error = np.max(Hz_var)
error = np.sum(Hz_var)
print(coef, error)
return error
def gen_krylov_basis(H, dim, init_state, system, orth=False):
krylov_basis = init_state.prod_basis()
current_state = krylov_basis
for n in range(0, dim):
next_state = np.dot(H, current_state)
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
krylov_basis = np.vstack((krylov_basis, next_state))
current_state = next_state
krylov_basis = np.transpose(krylov_basis)
if orth is False:
return krylov_basis
else:
if orth == "qr":
krylov_basis, temp = np.linalg.qr(krylov_basis)
else:
gs = gram_schmidt(krylov_basis)
gs.ortho()
krylov_basis = gs.ortho_basis
return krylov_basis
def max_variance(coef):
Hp_total = deepcopy(Hp[0])
for n in range(1,len(Hp)):
Hp_total = H_operations.add(Hp_total,Hp[n],np.array([1,coef[n-1]]))
Hm = Hp_total.herm_conj()
Hz = 1/2 * com(Hp_total.sector.matrix(),Hm.sector.matrix())
e,u = np.linalg.eigh(Hz)
psi = u[:,0]
from Calculations import gen_fsa_basis,gram_schmidt
fsa_dim = int(pxp.N)
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(),psi,fsa_dim)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
var_vals = np.zeros(np.size(fsa_basis,axis=1))
for n in range(0,np.size(var_vals,axis=0)):
var_vals[n] = np.real(var(Hz,fsa_basis[:,n]))
error = np.max(var_vals)
return error
def spacing_error(coef, pxp_config, pxxxp_config):
Hp = gen_Hp(pxp_config, pxp_config, coef)
Hm = np.conj(np.transpose(Hp))
Hz = 1 / 2 * com(Hp, Hm)
#find lowest weight state
e, u = np.linalg.eigh(Hz)
lowest_weight = u[:, 0]
z = zm_state(2, 1, pxp, 1)
fsa_basis = gen_fsa_basis(Hp, z.prod_basis(), pxp.N)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
if np.size(np.shape(fsa_basis)) == 2:
Hz_exp = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(Hz_exp, axis=0)):
Hz_exp[n] = exp(Hz, fsa_basis[:, n])
Hz_diff = np.zeros(np.size(Hz_exp) - 1)
for n in range(0, np.size(Hz_diff, axis=0)):
Hz_diff[n] = np.abs(Hz_exp[n + 1] - Hz_exp[n])
#spacing error
error_matrix = np.zeros((np.size(Hz_diff), np.size(Hz_diff)))
for n in range(0, np.size(error_matrix, axis=0)):
for m in range(0, np.size(error_matrix, axis=0)):
error_matrix[n, m] = np.abs(Hz_diff[n] - Hz_diff[m])
error = np.power(
np.trace(np.dot(error_matrix,
np.conj(np.transpose(error_matrix)))), 0.5)
print(coef, error)
return error
else:
return 1000
application_index_dual = np.vstack(
(application_index_dual, np.array([Im_app, Lp_app])))
current_state = np.dot(Lp.sector.matrix(k), tagged_state)
current_state = current_state / np.power(
np.vdot(current_state, current_state), 0.5)
su3_basis_dual = np.vstack((su3_basis_dual, current_state))
current_S = current_S - 1 / 2
Im_app = 0
Lp_app += 1
application_index_dual = np.vstack(
(application_index_dual, np.array([Im_app, Lp_app])))
su3_basis_dual = np.transpose(su3_basis_dual)
su3_basis = np.hstack((su3_basis, su3_basis_dual))
from Calculations import gram_schmidt
gs = gram_schmidt(su3_basis)
gs.ortho()
su3_basis = gs.ortho_basis
I3 = 1 / 2 * com(Ip_total.sector.matrix(k), Im_total.sector.matrix(k))
root3 = np.power(3, 0.5)
g8 = 1 / (2 *
root3) * (com(Kp_total.sector.matrix(k), Km_total.sector.matrix(k)) +
com(Lp_total.sector.matrix(k), Lm_total.sector.matrix(k)))
e, u = np.linalg.eigh(I3)
lw = u[:, 0]
#generate new su3 rep
su3_basis = lw
for n in range(0, np.size(application_index, axis=0)):
temp_state = lw
#need mapping from full basis to even/odd sub basis
for n in range(0, krylov_dim):
next_state_half_rep = gsa_Hp(current_state_half_rep)
next_state_full_rep = half_rep_to_full(next_state_half_rep, M_basis_map,
pxp_half, pxp)
gfsa_basis = np.vstack((gfsa_basis, next_state_full_rep))
# gs = gram_schmidt(np.transpose(gfsa_basis))
# gs.ortho()
# gfsa_basis = np.transpose(gs.ortho_basis)
current_state_half_rep = next_state_half_rep
gfsa_basis = np.transpose(gfsa_basis)
# gfsa_basis,temp = np.linalg.qr(gfsa_basis)
gs = gram_schmidt(gfsa_basis)
gs.ortho()
gfsa_basis = gs.ortho_basis
#project hamiltonians
H_krylov = np.dot(np.conj(np.transpose(krylov_basis)),
np.dot(H.sector.matrix(), krylov_basis))
H_fsa = np.dot(np.conj(np.transpose(fsa_basis)),
np.dot(H.sector.matrix(), fsa_basis))
H_gfsa = np.dot(np.conj(np.transpose(gfsa_basis)),
np.dot(H.sector.matrix(), gfsa_basis))
e_krylov, u_krylov = np.linalg.eigh(H_krylov)
e_fsa, u_fsa = np.linalg.eigh(H_fsa)
e_gfsa, u_gfsa = np.linalg.eigh(H_gfsa)
print(e_krylov)
# basis = np.hstack((L_cube_basis,basis)) # basis = np.hstack((basis,R_cube_basis)) # basis = np.hstack((L_cube_basis,basis)) # basis = np.hstack((basis,R_cube_basis)) basis = np.hstack((L_cube_basis, basis)) basis = np.hstack((basis, R_cube_basis)) basis = np.unique(basis, axis=1) # basis = np.hstack((basis,L_cube_basis)) # basis = np.hstack((basis,np.flip(R_cube_basis,axis=1))) #gram schmidt, QR ruins particle hole from Calculations import gram_schmidt gs = gram_schmidt(basis) gs.ortho() basis = gs.ortho_basis # include Neel fsa (orig) #fsa Hamiltonian, H= H+ + H- Hp1 = Hamiltonian(pxp) Hp1.site_ops[1] = np.array([[0, 1], [0, 0]]) Hp1.model = np.array([[1]]) Hp1.model_coef = np.array([1]) Hp1.gen(parity=0) Hp2 = Hamiltonian(pxp) Hp2.site_ops[1] = np.array([[0, 0], [1, 0]]) Hp2.model = np.array([[1]]) Hp2.model_coef = np.array([1]) Hp2.gen(parity=1)
def gen_su3Basis(coef):
c = 0
Ip_total = deepcopy(Ip[0])
for n in range(1, len(Ip)):
Ip_total = H_operations.add(Ip_total, Ip[n],
np.array([1, coef[c + n - 1]]))
Im_total = deepcopy(Im[0])
for n in range(1, len(Im)):
Im_total = H_operations.add(Im_total, Im[n],
np.array([1, coef[c + n - 1]]))
c += len(Ip) - 1
Kp_total = deepcopy(Kp[0])
for n in range(1, len(Kp)):
Kp_total = H_operations.add(Kp_total, Kp[n],
np.array([1, coef[c + n - 1]]))
Km_total = deepcopy(Km[0])
for n in range(1, len(Km)):
Km_total = H_operations.add(Km_total, Km[n],
np.array([1, coef[c + n - 1]]))
c += len(Kp) - 1
Lp_total = deepcopy(Lp[0])
for n in range(1, len(Lp)):
Lp_total = H_operations.add(Lp_total, Lp[n],
np.array([1, coef[c + n - 1]]))
Lm_total = deepcopy(Lm[0])
for n in range(1, len(Lm)):
Lm_total = H_operations.add(Lm_total, Lm[n],
np.array([1, coef[c + n - 1]]))
H = H_operations.add(Ip_total, Im_total, np.array([1j, -1j]))
H = H_operations.add(H, Kp_total, np.array([1, -1j]))
H = H_operations.add(H, Km_total, np.array([1, 1j]))
H = H_operations.add(H, Lp_total, np.array([1, 1j]))
H = H_operations.add(H, Lm_total, np.array([1, -1j]))
#su3 rep
#0th order rep (no perts)
root3 = np.power(3, 0.5)
I3 = 1 / 2 * com(Ip[0].sector.matrix(k), Im[0].sector.matrix(k))
g8 = 1 / (2 *
root3) * (com(Kp[0].sector.matrix(k), Km[0].sector.matrix(k)) +
com(Lp[0].sector.matrix(k), Lm[0].sector.matrix(k)))
def exp(Q, psi):
return np.real(np.vdot(psi, np.dot(Q, psi)))
def var(Q, psi):
Q2 = np.dot(Q, Q)
return exp(Q2, psi) - (exp(Q, psi))**2
e, u = np.linalg.eigh(I3)
lw = u[:, 0]
hw = u[:, np.size(u, axis=1) - 1]
#generate su3 representation by applying I+,L- to lw state
su3_basis_states = dict()
su3_basis = lw
current_state = su3_basis
i3_lw = exp(I3, lw)
g8_hw = exp(g8, lw)
current_S = np.abs(i3_lw)
Ip_app = 0
Lm_app = 0
application_index = np.zeros(2)
while np.abs(current_S) > 1e-5:
no_ip_apps = int(2 * current_S)
tagged_state = current_state
for n in range(0, no_ip_apps):
Ip_app = Ip_app + 1
next_state = np.dot(Ip[0].sector.matrix(k), current_state)
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
su3_basis = np.vstack((su3_basis, next_state))
current_state = next_state
application_index = np.vstack(
(application_index, np.array([Ip_app, Lm_app])))
current_state = np.dot(Lm[0].sector.matrix(k), tagged_state)
current_state = current_state / np.power(
np.vdot(current_state, current_state), 0.5)
su3_basis = np.vstack((su3_basis, current_state))
current_S = current_S - 1 / 2
Ip_app = 0
Lm_app += 1
application_index = np.vstack(
(application_index, np.array([Ip_app, Lm_app])))
su3_basis = np.transpose(su3_basis)
#generate su3 dual representation (starting from highest weight state) representation by applying I-,L+ to lw state
su3_basis_dual = hw
current_state = su3_basis_dual
i3_hw = exp(I3, hw)
g8_lw = exp(g8, hw)
current_S = np.abs(i3_hw)
Im_app = 0
Lp_app = 0
application_index_dual = np.zeros(2)
while np.abs(current_S) > 1e-5:
no_im_apps = int(2 * current_S)
tagged_state = current_state
for n in range(0, no_im_apps):
Im_app = Im_app + 1
next_state = np.dot(Im[0].sector.matrix(k), current_state)
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
su3_basis_dual = np.vstack((su3_basis_dual, next_state))
current_state = next_state
application_index_dual = np.vstack(
(application_index_dual, np.array([Im_app, Lp_app])))
current_state = np.dot(Lp[0].sector.matrix(k), tagged_state)
current_state = current_state / np.power(
np.vdot(current_state, current_state), 0.5)
su3_basis_dual = np.vstack((su3_basis_dual, current_state))
current_S = current_S - 1 / 2
Im_app = 0
Lp_app += 1
application_index_dual = np.vstack(
(application_index_dual, np.array([Im_app, Lp_app])))
su3_basis_dual = np.transpose(su3_basis_dual)
su3_basis = np.hstack((su3_basis, su3_basis_dual))
from Calculations import gram_schmidt
gs = gram_schmidt(su3_basis)
gs.ortho()
su3_basis = gs.ortho_basis
return su3_basis
def subspace_variance(coef):
c=0
Ip_total = deepcopy(Ip[0])
for n in range(1,len(Ip)):
Ip_total = H_operations.add(Ip_total,Ip[n],np.array([1,coef[c+n-1]]))
Im_total = deepcopy(Im[0])
for n in range(1,len(Im)):
Im_total = H_operations.add(Im_total,Im[n],np.array([1,coef[c+n-1]]))
c += len(Ip)-1
Kp_total = deepcopy(Kp[0])
for n in range(1,len(Kp)):
Kp_total = H_operations.add(Kp_total,Kp[n],np.array([1,coef[c+n-1]]))
Km_total = deepcopy(Km[0])
for n in range(1,len(Km)):
Km_total = H_operations.add(Km_total,Km[n],np.array([1,coef[c+n-1]]))
c += len(Kp)-1
Lp_total = deepcopy(Lp[0])
for n in range(1,len(Lp)):
Lp_total = H_operations.add(Lp_total,Lp[n],np.array([1,coef[c+n-1]]))
Lm_total = deepcopy(Lm[0])
for n in range(1,len(Lm)):
Lm_total = H_operations.add(Lm_total,Lm[n],np.array([1,coef[c+n-1]]))
H=H_operations.add(Ip_total,Im_total,np.array([1j,-1j]))
H=H_operations.add(H,Kp_total,np.array([1,-1j]))
H=H_operations.add(H,Km_total,np.array([1,1j]))
H=H_operations.add(H,Lp_total,np.array([1,1j]))
H=H_operations.add(H,Lm_total,np.array([1,-1j]))
#su3 rep
#0th order rep (no perts)
root3 = np.power(3,0.5)
I3 = 1/2 * com(Ip[0].sector.matrix(k),Im[0].sector.matrix(k))
g8 = 1/(2*root3) * ( com(Kp[0].sector.matrix(k),Km[0].sector.matrix(k)) + com(Lp[0].sector.matrix(k),Lm[0].sector.matrix(k)) )
def exp(Q,psi):
return np.real(np.vdot(psi,np.dot(Q,psi)))
def var(Q,psi):
Q2 = np.dot(Q,Q)
return exp(Q2,psi)-(exp(Q,psi))**2
e,u = np.linalg.eigh(I3)
lw = u[:,0]
hw = u[:,np.size(u,axis=1)-1]
#generate su3 representation by applying I+,L- to lw state
su3_basis_states = dict()
su3_basis = lw
current_state = su3_basis
i3_lw = exp(I3,lw)
g8_hw = exp(g8,lw)
current_S = np.abs(i3_lw)
Ip_app= 0
Lm_app= 0
application_index = np.zeros(2)
while np.abs(current_S)>1e-5:
no_ip_apps = int(2*current_S)
tagged_state = current_state
for n in range(0,no_ip_apps):
Ip_app = Ip_app + 1
next_state = np.dot(Ip[0].sector.matrix(k),current_state)
next_state = next_state / np.power(np.vdot(next_state,next_state),0.5)
su3_basis = np.vstack((su3_basis,next_state))
current_state = next_state
application_index = np.vstack((application_index,np.array([Ip_app,Lm_app])))
current_state = np.dot(Lm[0].sector.matrix(k),tagged_state)
current_state = current_state / np.power(np.vdot(current_state,current_state),0.5)
su3_basis = np.vstack((su3_basis,current_state))
current_S = current_S - 1/2
Ip_app = 0
Lm_app += 1
application_index = np.vstack((application_index,np.array([Ip_app,Lm_app])))
su3_basis = np.transpose(su3_basis)
#generate su3 dual representation (starting from highest weight state) representation by applying I-,L+ to lw state
su3_basis_dual = hw
current_state = su3_basis_dual
i3_hw = exp(I3,hw)
g8_lw = exp(g8,hw)
current_S = np.abs(i3_hw)
Im_app= 0
Lp_app= 0
application_index_dual = np.zeros(2)
while np.abs(current_S)>1e-5:
no_im_apps = int(2*current_S)
tagged_state = current_state
for n in range(0,no_im_apps):
Im_app = Im_app + 1
next_state = np.dot(Im[0].sector.matrix(k),current_state)
next_state = next_state / np.power(np.vdot(next_state,next_state),0.5)
su3_basis_dual = np.vstack((su3_basis_dual,next_state))
current_state = next_state
application_index_dual = np.vstack((application_index_dual,np.array([Im_app,Lp_app])))
current_state = np.dot(Lp[0].sector.matrix(k),tagged_state)
current_state = current_state / np.power(np.vdot(current_state,current_state),0.5)
su3_basis_dual = np.vstack((su3_basis_dual,current_state))
current_S = current_S - 1/2
Im_app = 0
Lp_app += 1
application_index_dual = np.vstack((application_index_dual,np.array([Im_app,Lp_app])))
su3_basis_dual = np.transpose(su3_basis_dual)
su3_basis = np.hstack((su3_basis,su3_basis_dual))
from Calculations import gram_schmidt
gs = gram_schmidt(su3_basis)
gs.ortho()
su3_basis = gs.ortho_basis
I3 = 1/2 * com(Ip_total.sector.matrix(k),Im_total.sector.matrix(k))
root3=np.power(3,0.5)
g8 = 1/(2*root3)*( com(Kp_total.sector.matrix(k),Km_total.sector.matrix(k)) + com(Lp_total.sector.matrix(k),Lm_total.sector.matrix(k)) )
e,u = np.linalg.eigh(I3)
lw = u[:,0]
#generate new su3 rep
su3_basis= lw
for n in range(0,np.size(application_index,axis=0)):
temp_state = lw
for u in range(0,int(application_index[n,1])):
temp_state = np.dot(Lm_total.sector.matrix(k),temp_state)
for u in range(0,int(application_index[n,0])):
temp_state = np.dot(Ip_total.sector.matrix(k),temp_state)
temp_state = temp_state / np.power(np.vdot(temp_state,temp_state),0.5)
su3_basis = np.vstack((su3_basis,temp_state))
su3_basis = np.transpose(su3_basis)
#generate new su3 rep dual
su3_basis_dual= hw
for n in range(0,np.size(application_index_dual,axis=0)):
temp_state = hw
for u in range(0,int(application_index_dual[n,1])):
temp_state = np.dot(Lp_total.sector.matrix(k),temp_state)
for u in range(0,int(application_index_dual[n,0])):
temp_state = np.dot(Im_total.sector.matrix(k),temp_state)
temp_state = temp_state / np.power(np.vdot(temp_state,temp_state),0.5)
su3_basis_dual = np.vstack((su3_basis_dual,temp_state))
su3_basis_dual = np.transpose(su3_basis_dual)
su3_basis = np.hstack((su3_basis,su3_basis_dual))
from Calculations import gram_schmidt
gs = gram_schmidt(su3_basis)
gs.ortho()
su3_basis = gs.ortho_basis
H2 = np.dot(H.sector.matrix(k),H.sector.matrix(k))
H2_fsa = np.dot(np.conj(np.transpose(su3_basis)),np.dot(H2,su3_basis))
H_fsa = np.dot(np.conj(np.transpose(su3_basis)),np.dot(H.sector.matrix(k),su3_basis))
subspace_variance = np.real(np.trace(H2_fsa-np.dot(H_fsa,H_fsa)))
error = subspace_variance / np.size(su3_basis,axis=1)
print(coef,error)
e,u = np.linalg.eigh(H_fsa)
plt.scatter(e,np.log10(np.abs(u[0,:])**2),marker="x",color="red",s=100)
# np.save("pcp,2ndOrderSU3,coef,"+str(pxp.N),coef)
# if (np.abs(coef)>0.5).any():
# return 1000
# else:
return error
