def fidelity_erorr(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]
H = H_operations.add(Hp_total, Hm, np.array([1, 1]))
H.sector.find_eig(k)
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))), psi)
t = np.arange(0, 6, 0.001)
# t=np.arange(0,20,0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
evolved_state = time_evolve_state(psi_energy, H.sector.eigvalues(k),
t[n])
f[n] = np.abs(np.vdot(evolved_state, psi_energy))**2
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f0 = np.max(f[cut:])
# plt.plot(t,f)
# plt.show()
# res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(),t),method="golden",bracket=(2.5,5.5))
# f0 = fidelity_eval(psi_energy,H.sector.eigvalues(),res.x)
return 1 - f0
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()
z=zm_state(3,1,pxp)
from Calculations import gen_fsa_basis
fsa_dim = int(2*pxp.N/3)
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(),z.prod_basis(),fsa_dim)
# for n in range(0,np.size(fsa_basis,axis=1)):
# for m in range(0,np.size(fsa_basis,axis=1)):
# temp = np.abs(np.vdot(fsa_basis[:,n],fsa_basis[:,m]))
# if temp > 1e-5:
# print(temp,n,m)
fsa_basis,temp = np.linalg.qr(fsa_basis)
H2 = np.dot(H.sector.matrix(),H.sector.matrix())
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(),fsa_basis))
subspace_variance = np.real(np.trace(H2_fsa-np.dot(H_fsa,H_fsa)))
return subspace_variance
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 fidelity_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_total = Hp_total.herm_conj()
H = H_operations.add(Hp_total, Hm_total, np.array([1, 1]))
H.sector.find_eig(k)
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors(k))), psi_mom)
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
evolved_state = time_evolve_state(psi_energy, H.sector.eigvalues(k),
t[n])
f[n] = np.abs(np.vdot(evolved_state, psi_energy))**2
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.5:
cut = n
break
f_max = np.max(f[cut:])
error = 1 - f_max
# res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(k),t),method="golden")
# f0 = fidelity_eval(psi_energy,H.sector.eigvalues(k),res.x)
# error = 1-f0
print(coef, error)
# if (np.abs(coef)>1).any():
# return 1000
# else:
return error
def fidelity_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 = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(2, 1, pxp, 1)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
t = np.arange(0, 10, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
# plt.plot(t,f)
# plt.show()
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f_max = np.max(f[cut:])
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
else:
return -f_max
def var_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 = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm)
z = zm_state(2, 1, pxp, 1)
fsa_basis = z.prod_basis()
current_state = fsa_basis
for n in range(0, pxp.N):
next_state = np.dot(Hp_total.sector.matrix(), current_state)
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
fsa_basis = np.vstack((fsa_basis, next_state))
current_state = next_state
fsa_basis = np.transpose(fsa_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)
print(coef, error)
return error
def spacing_error(coef, psi):
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 = np.conj(np.transpose(Hp_total.sector.matrix()))
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm)
from Calculations import gen_fsa_basis
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(), psi, pxp.N)
Hz_exp = np.zeros(np.size(fsa_basis, axis=1))
for n in range(0, np.size(fsa_basis, axis=1)):
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] = Hz_exp[n + 1] - Hz_exp[n]
M = np.zeros((np.size(Hz_diff), np.size(Hz_diff)))
for n in range(0, np.size(M, axis=0)):
for m in range(0, np.size(M, axis=0)):
M[n, m] = np.abs(Hz_diff[n] - Hz_diff[m])
error = np.power(np.trace(np.dot(M, np.conj(np.transpose(M)))), 0.5)
print(coef, error)
return error
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 overlap_error(coef):
# coef = coef[0]
H = H_operations.add(H0, V, np.array([1, coef]))
H.sector.find_eig()
overlap_no_log = np.abs(H.sector.eigvectors()[pxp.keys[z.ref], :])**2
overlap = np.log10(overlap_no_log)
scar_indices_perturbed = np.flip(
get_top_band_indices(H.sector.eigvalues(), overlap, pxp.N, 200, 150,
0.8))
# check got right scars
# plt.scatter(H.sector.eigvalues(),overlap)
# for n in range(0,np.size(scar_indices_perturbed,axis=0)):
# plt.scatter(H.sector.eigvalues()[scar_indices_perturbed[n]],overlap[scar_indices_perturbed[n]],marker="x",color="red",s=100)
# plt.show()
for n in range(0, np.size(scar_indices_perturbed, axis=0)):
overlap_no_log = np.delete(overlap_no_log,
scar_indices_perturbed[n],
axis=0)
cost = np.sum(overlap_no_log)
# cost = np.sum(scar_overlap_perturbed-scar_overlap)
print(coef, cost)
return cost
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(), Hm.sector.matrix())
z = zm_state(2, 1, pxp, 1)
from Calculations import gen_fsa_basis
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(), z.prod_basis(), pxp.N)
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 fidelity_error(coef):
np.save("NEWising,pert_coef," + str(pxp.N), 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 = np.conj(np.transpose(Hp_total.sector.matrix()))
Hz = 1 / 2 * com(Hp_total.sector.matrix(), Hm)
e, u = np.linalg.eigh(Hz)
psi = u[:, 0]
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
psi_energy = np.dot(np.conj(np.transpose(u)), psi)
t = np.arange(0, 10, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
for n in range(0, np.size(f, axis=0)):
if f[n] < 0.1:
cut = n
break
f_max = np.max(f[cut:])
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
else:
return -f_max
def fidelity_error(coef, plot=False):
coef = coef[0]
H = H_operations.add(H0, V, np.array([1, coef]))
H = H.sector.matrix()
e, u = np.linalg.eigh(H)
z = zm_state(4, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
if plot is True:
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
f[n] = -fidelity_eval(psi_energy, e, t[n])
plt.plot(t, f)
plt.show()
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(4.5, 5.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
if res.x < 1e-5:
return 1000
else:
return -f
def fidelity_erorr(coef):
coef = coef[0]
Hp_total = deepcopy(Hp[0])
Hp_total = H_operations.add(Hp_total,Hp[1],np.array([1,coef]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(2,2,pxp,1)
psi_energy = np.dot(np.conj(np.transpose(H.sector.eigvectors())),z.prod_basis())
res = minimize_scalar(lambda t: -fidelity_eval(psi_energy,H.sector.eigvalues(),t),method="golden",bracket=(4.5,5.5))
f0 = fidelity_eval(psi_energy,H.sector.eigvalues(),res.x)
print(coef,f0)
return 1-f0
def subspace_variance(coef):
coef = coef[0]
Hp_total = deepcopy(Hp[0])
Hp_total = H_operations.add(Hp_total,Hp[1],np.array([1,coef]))
Hm = Hp_total.herm_conj()
H = H_operations.add(Hp_total,Hm,np.array([1,1]))
H.sector.find_eig()
z=zm_state(2,2,pxp,1)
from Calculations import gen_fsa_basis
fsa_dim = 2*pxp.N
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(),z.prod_basis(),fsa_dim)
H2 = np.dot(H.sector.matrix(),H.sector.matrix())
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(),fsa_basis))
subspace_variance = np.real(np.trace(H2_fsa-np.dot(H_fsa,H_fsa)))
return subspace_variance
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 = np.conj(np.transpose(Hp_total.sector.matrix()))
Hp0 = Hp_total.sector.matrix()
Hm0 = np.conj(np.transpose(Hp0))
Hz = 1 / 2 * com(Hp0, Hm0)
#find lowest weight state
e, u = np.linalg.eigh(Hz)
lowest_weight = u[:, 0]
z = zm_state(2, 1, pxp, 1)
fsa_basis = z.prod_basis()
current_state = fsa_basis
fsa_dim = pxp.N
for n in range(0, fsa_dim):
next_state = np.dot(Hp0, current_state)
if np.abs(np.vdot(next_state, next_state)) > 1e-5:
next_state = next_state / np.power(np.vdot(next_state, next_state),
0.5)
fsa_basis = np.vstack((fsa_basis, next_state))
current_state = next_state
else:
break
fsa_basis = np.transpose(fsa_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(Hz_diff, axis=0)):
for m in range(0, np.size(Hz_diff, 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
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())
z = zm_state(2, 1, pxp, 1)
from Calculations import gen_fsa_basis
fsa_basis = gen_fsa_basis(Hp_total.sector.matrix(), z.prod_basis(), pxp.N)
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):
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 = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(3, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
overlap = np.log10(np.abs(psi_energy)**2)
scar_indices = get_top_band_indices(e,
overlap,
int(2 * N / 3),
150,
200,
e_diff=0.5)
# plt.scatter(e,overlap)
# for n in range(0,np.size(scar_indices,axis=0)):
# plt.scatter(e[scar_indices[n]],overlap[scar_indices[n]],marker="x",s=100,color="red")
# plt.show()
scar_e = np.zeros(np.size(scar_indices))
for n in range(0, np.size(scar_indices, axis=0)):
scar_e[n] = e[scar_indices[n]]
diffs = np.zeros(np.size(scar_e) - 1)
for n in range(0, np.size(diffs, axis=0)):
diffs[n] = scar_e[n + 1] - scar_e[n]
diff_matrix = np.zeros((np.size(diffs), np.size(diffs)))
for n in range(0, np.size(diff_matrix, axis=0)):
for m in range(0, np.size(diff_matrix, axis=0)):
diff_matrix[n, m] = diffs[n] - diffs[m]
error = np.power(
np.trace(np.dot(diff_matrix, np.conj(np.transpose(diff_matrix)))), 0.5)
print(coef, error)
print(scar_e)
# print(coef)
# if (np.abs(coef).any())>0.5:
# return 1000
# else:
return error
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 krylov_su2_coupling_error(coef):
coef = coef[0]
H = H_operations.add(H0,V,np.array([1,coef]))
z=zm_state(2,1,pxp)
krylov_basis = gen_krylov_basis(H.sector.matrix(),pxp.N,z.prod_basis(),pxp,orth="qr")
H_krylov = np.dot(np.conj(np.transpose(krylov_basis)),np.dot(H.sector.matrix(),krylov_basis))
couplings = np.diag(H_krylov,1)
s = pxp.N/4
m = np.arange(-s,s)
su2_couplings_half = np.power(s*(s+1)-m*(m+1),0.5)
s = pxp.N/2
m = np.arange(-s,s)
su2_couplings_full = np.power(s*(s+1)-m*(m+1),0.5)
coupling_diff_full = couplings - su2_couplings_full
error = np.power(np.abs(np.vdot(coupling_diff_full,coupling_diff_full)),0.5)
# error = np.abs(couplings[3] - su2_couplings_half[3])
print(coef,error)
return error
def fidelity_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 = np.conj(np.transpose(Hp_total.sector.matrix()))
H = Hp_total.sector.matrix() + Hm
e, u = np.linalg.eigh(H)
z = zm_state(3, 1, pxp)
psi_energy = np.dot(np.conj(np.transpose(u)), z.prod_basis())
res = minimize_scalar(lambda t: fidelity_eval(psi_energy, e, t),
method="golden",
bracket=(2.5, 3.5))
f = -fidelity_eval(psi_energy, e, res.x)
print(coef, f)
# print(f)
if res.x < 1e-5:
return 1000
if (np.abs(coef) > 0.5).any():
return 1000
return -f
Ip.gen(k) Im.gen(k) Kp.gen(k) Km.gen(k) Lp.gen(k) Lm.gen(k) Ip_pert.gen(k) Im_pert.gen(k) Kp_pert.gen(k) Km_pert.gen(k) Lp_pert.gen(k) Lm_pert.gen(k) coef = 0 # coef = -0.0827840215 Ip_total = H_operations.add(Ip, Ip_pert, np.array([1, coef])) Im_total = H_operations.add(Im, Im_pert, np.array([1, coef])) Kp_total = H_operations.add(Kp, Kp_pert, np.array([1, coef])) Km_total = H_operations.add(Km, Km_pert, np.array([1, coef])) Lp_total = H_operations.add(Lp, Lp_pert, np.array([1, coef])) Lm_total = H_operations.add(Lm, Lm_pert, np.array([1, coef])) 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])) H.sector.find_eig(k) exact_energy = H.sector.eigvalues(k) exact_overlap = eig_overlap(z, H, k).eval()
H0.model = np.array([[1]])
H0.model_coef = np.array([1])
H1 = Hamiltonian(pxp, pxp_syms)
H1.site_ops[1] = np.array([[0, 1], [1, 0]])
H1.model = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 1, 0]])
H1.model_coef = np.array([1, 1, 1, 1])
H1.uc_size = np.array([3, 3, 3, 3])
H1.uc_pos = np.array([1, 2, 2, 1])
k = [0]
H0.gen(k)
H1.gen(k)
# H0.gen()
# H1.gen()
H = H_operations.add(H0, H1, np.array([1, -1]))
from Calculations import plot_adjacency_graph, connected_comps
comp = connected_comps(H, k)
# comp = connected_comps(H)
comp.find_connected_components()
subspace_sizes = dict()
for n in range(0, len(comp.components)):
print("\n")
print(np.size(comp.components[n]))
for m in range(0, np.size(comp.components[n], axis=0)):
print(pxp.basis[pxp.keys[comp.components[n][m]]])
size = np.size(comp.components[n])
if size not in list(subspace_sizes.keys()):
subspace_sizes[size] = 1
else:
Hp[9].uc_pos = np.array([0, 0, 1, 1])
for n in range(0, len(Hp)):
Hp[n].gen()
# coef = np.array([0.0008,-1.43,0.0979,0.0980])
# coef = np.array([0.1897,0.2322,0.0312,0.0014,-0.0023,-0.00492,0.0056,0.0006,-0.0134,0.0130,-0.0138,-0.0253,-0.0623,0.0166,-0.0281,0.0200])
coef = np.array([
0.11135, 0.000217, -0.000287, -0.00717, 0.00827, 0.00336, 0.00429, 0.0103,
0.00118
])
from copy import deepcopy
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]]))
Hp = Hp_total.sector.matrix()
Hm = np.conj(np.transpose(Hp))
H = Hp + Hm
z = zm_state(2, 1, pxp, 1)
e, u = np.linalg.eigh(H)
overlap = np.log10(np.abs(u[pxp.keys[z.ref], :])**2)
psi_energy = np.conj(u[pxp.keys[z.ref], :])
t = np.arange(0, 20, 0.01)
f = np.zeros(np.size(t))
for n in range(0, np.size(t, axis=0)):
evolved_state = time_evolve_state(psi_energy, e, t[n])
f[n] = np.abs(np.vdot(evolved_state, psi_energy))**2
if np.abs(psi[m])>1e-5:
refs_non_zeros = np.append(refs_non_zeros,pxp.basis_refs[m])
refs_non_zeros = np.unique(np.sort(refs_non_zeros))
return refs_non_zeros
#PXP+PPXP
from Hamiltonian_Classes import H_operations
H0 = spin_Hamiltonian(pxp,"x")
V = Hamiltonian(pxp)
V.site_ops[1] = np.array([[0,1/2],[1/2,0]])
V.site_ops[2] = np.array([[-1/2,0],[0,1/2]])
V.model = np.array([[2,0,1,0],[0,1,0,2]])
V.model_coef = np.array([1,1])
H0.gen()
V.gen()
H = H_operations.add(H0,V,np.array([1,-0.02]))
H.sector.find_eig()
H = spin_Hamiltonian(pxp,"x")
H.gen()
H.sector.find_eig()
# N=10
# root_refs = find_root_refs(np.array([3,0]),np.array([3,1]),H,sector_refs,from_sector,pxp,[])
# basis = subcube_basis(root_refs,"Left",4)
# refs_found = non_zero_ref_in_basis(basis)
# print("\n")
# root_refs = find_root_refs(np.array([0,3]),np.array([1,3]),H,sector_refs,from_sector,pxp,refs_found)
# if np.size(root_refs)>0:
# temp = subcube_basis(root_refs,"Right",4)
# P+P on even sites
pe = Hamiltonian(pxp,pxp_syms)
# pe.site_ops[1] = np.array([[0,1],[0,0]])
pe.site_ops[1] = np.array([[0,1j,0],[0,0,1j],[1j,0,0]])
pe.model = np.array([[0,1,0]])
pe.model_coef = np.array([1])
pe.gen(parity=1)
#P-P on odd sites
mo = Hamiltonian(pxp,pxp_syms)
# mo.site_ops[1] = np.array([[0,0],[1,0]])
mo.site_ops[1] = np.array([[0,0,-1j],[-1j,0,0],[0,-1j,0]])
mo.model = np.array([[0,1,0]])
mo.model_coef = np.array([1])
mo.gen(parity=0)
#Raising op
Hp = H_operations.add(pe,mo,np.array([1,1]))
Hp = Hp.sector.matrix()
Hm = np.conj(np.transpose(Hp))
fsa_basis = z.prod_basis()
current_state = fsa_basis
for n in range(0,krylov_dim):
next_state = np.dot(Hm,current_state)
next_state = next_state / np.power(np.vdot(next_state,next_state),0.5)
fsa_basis = np.vstack((fsa_basis,next_state))
current_state = next_state
fsa_basis = np.transpose(fsa_basis)
# fsa_basis,temp = np.linalg.qr(fsa_basis)
gs = gram_schmidt(fsa_basis)
gs.ortho()
fsa_basis = gs.ortho_basis
res = minimize(lambda coef: spacing_error(coef), method="Nelder-Mead", x0=coef)
coef = res.x
# coef = np.zeros(1)
# # coef = np.load("./data/pxp,z4,pert_coef.npy")
# # coef = res.x
# # coef[1] = -1
# error = spacing_error(coef)
# print("ERROR VALUE: "+str(error))
print(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]]))
Hp_total = H_operations.add(Hp_total, Hp[1], np.array([1, coef]))
Hp = Hp_total.sector.matrix()
Hm = np.conj(np.transpose(Hp))
H = Hp + Hm
# H = Hamiltonian(pxp)
# H.site_ops[1] = np.array([[0,1],[1,0]])
# H.model = np.array([[0,1,0],[0,1,1,1,0]])
# H.model_coef = np.array([1,coef])
# H.gen()
# H = H.sector.matrix()
def com(a, b):
return np.dot(a, b) - np.dot(b, a)
Hpo.model_coef = np.array([1])
Hpo.gen(parity=1)
Hme = Hamiltonian(pxp, pxp_syms)
Hme.site_ops[1] = np.array([[0, 0], [1, 0]])
Hme.model = np.array([[0, 1, 0]])
Hme.model_coef = np.array([1])
Hme.gen(parity=0)
Hmo = Hamiltonian(pxp, pxp_syms)
Hmo.site_ops[1] = np.array([[0, 0], [1, 0]])
Hmo.model = np.array([[0, 1, 0]])
Hmo.model_coef = np.array([1])
Hmo.gen(parity=1)
Hp = H_operations.add(Hpe, Hmo, np.array([1, 1]))
Hm = H_operations.add(Hme, Hpo, np.array([1, 1]))
def com(a, b):
return np.dot(a, b) - np.dot(b, a)
Hz = com(Hp.sector.matrix(), Hm.sector.matrix())
z = zm_state(2, 1, pxp)
z_prod_basis = z.prod_basis()
fsa_basis = z.prod_basis()
current_state = fsa_basis
for n in range(0, pxp.N):
new_state = np.dot(Hp.sector.matrix(), current_state)
V1_ops[2].site_ops[1] = np.array([[0, 1], [1, 0]])
V1_ops[2].model = np.array([[0, 1, 0, 0]])
V1_ops[2].model_coef = np.array([1])
for n in range(0, np.size(k)):
V1_ops[2].gen(k_vec=k[n], uc_size=3, uc_pos=2)
V1_ops[3] = Hamiltonian(pxp, pxp_syms)
V1_ops[3].site_ops[1] = np.array([[0, 1], [1, 0]])
V1_ops[3].model = np.array([[0, 0, 1, 0]])
V1_ops[3].model_coef = np.array([1])
for n in range(0, np.size(k)):
V1_ops[3].gen(k_vec=k[n], uc_size=3, uc_pos=1)
V1 = V1_ops[0]
for n in range(1, len(V1_ops)):
V1 = H_operations.add(V1, V1_ops[n], np.array([1, 1]))
V2_ops = dict()
V2_ops[0] = Hamiltonian(pxp, pxp_syms)
V2_ops[0].site_ops[1] = np.array([[0, 1], [1, 0]])
V2_ops[0].model = np.array([[0, 0, 1, 0]])
V2_ops[0].model_coef = np.array([1])
for n in range(0, np.size(k)):
V2_ops[0].gen(k_vec=k[n], uc_size=3, uc_pos=0)
V2_ops[1] = Hamiltonian(pxp, pxp_syms)
V2_ops[1].site_ops[1] = np.array([[0, 1], [1, 0]])
V2_ops[1].model = np.array([[0, 1, 0, 0]])
V2_ops[1].model_coef = np.array([1])
for n in range(0, np.size(k)):
V2_ops[1].gen(k_vec=k[n], uc_size=3, uc_pos=0)
#FSA basis
# P+P on even sites
pe = Hamiltonian(pxp, pxp_syms)
pe.site_ops[1] = np.array([[0, 1, 1j], [-1, 0, 0], [-1j, 0, 0]])
pe.model = np.array([[0, 1, 0]])
pe.model_coef = np.array([1])
pe.gen(parity=1)
#P-P on odd sites
mo = Hamiltonian(pxp, pxp_syms)
mo.site_ops[1] = np.array([[0, -1, 1j], [1, 0, 0], [-1j, 0, 0]])
mo.model = np.array([[0, 1, 0]])
mo.model_coef = np.array([1])
mo.gen(parity=0)
#Raising op
Hp = H_operations.add(pe, mo, np.array([1, 1]))
Hp = Hp.sector.matrix()
Hm = np.conj(np.transpose(Hp))
def com(a, b):
return np.dot(a, b) - np.dot(b, a)
Hz = 1 / 2 * com(Hp, Hm)
e, u = np.linalg.eigh(Hz)
psi = u[:, 0]
# e,u = np.linalg.eigh(Hz)
# from Diagnostics import print_wf
# for n in range(0,np.size(u,axis=0)):
# if np.abs(e[n]) < 1e-5:
Hp_test0.site_ops[2] = np.array([[0, 1], [0, 0]])
Hp_test0.model = np.array([[0, 1, 0], [0, 2, 0]])
Hp_test0.model_coef = np.array([1, 1])
Hp_test0.uc_size = np.array([2, 2])
Hp_test0.uc_pos = np.array([1, 0])
Hp_test = Hamiltonian(pxp)
Hp_test.site_ops[1] = np.array([[0, 0], [1, 0]])
Hp_test.site_ops[2] = np.array([[0, 1], [0, 0]])
Hp_test.model = np.array([[0, 2, 1, 2, 0]])
Hp_test.model_coef = np.array([1])
Hp_test0.gen()
Hp_test.gen()
from Hamiltonian_Classes import H_operations
Hp_test = H_operations.add(Hp_test0, Hp_test, np.array([1, coef_f0]))
print((np.abs(Hp_test.sector.matrix() - Hp) < 1e-5).all())
Hz = 1 / 2 * com(Hp, Hm)
e, u = np.linalg.eigh(Hz)
z = zm_state(2, 1, pxp, 1)
lw = u[:, 0]
print("\n|<lw | Z_2 > |")
print(np.abs(np.vdot(lw, z.prod_basis())))
print("\n")
from Calculations import gen_fsa_basis, gram_schmidt
fsa_basis = gen_fsa_basis(Hp, z.prod_basis(), pxp.N)
gs = gram_schmidt(fsa_basis)
gs.ortho()
