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 = 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
e,u = np.linalg.eigh(H_fsa)
fsa_overlap = np.log10(np.abs(u[0,:])**2)
fsa_energy = e
plt.scatter(exact_energy,exact_overlap)
plt.scatter(fsa_energy,fsa_overlap,marker="x",color="red",s=100)
plt.show()
t=np.arange(0,20,0.01)
f=fidelity(z,H,"use sym").eval(t,z)
plt.plot(t,f)
plt.show()
#identify scar states for entropy highlight
scar_indices = get_top_band_indices(exact_energy,exact_overlap,pxp.N,100,100,e_diff = 0.5)
#check identified right states
plt.scatter(exact_energy,exact_overlap)
for n in range(0,np.size(scar_indices,axis=0)):
plt.scatter(exact_energy[scar_indices[n]],exact_overlap[scar_indices[n]],marker="D",color="green",alpha=0.5,s=100)
plt.show()
U = pxp_syms.basis_transformation(k[0])
eigvectors_comp = np.dot(U,H.sector.eigvectors(k[0]))
fsa_eigs_comp = np.dot(U,np.dot(fsa_basis,u))
#entropy
ent_vals = np.zeros(np.size(eigvectors_comp,axis=1))
ent = entropy(pxp)
pbar=ProgressBar()
for n in pbar(range(0,np.size(ent_vals,axis=0))):
def subspace_varianceSu2(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_basis = gen_su3Basis(coef)
# restrict to 2N+1 basis with largest overlap with scar states
# identify 2N+1 scars from H
H.sector.find_eig(k)
overlap = eig_overlap(z, H, k).eval()
from Calculations import get_top_band_indices
scar_indices = get_top_band_indices(H.sector.eigvalues(k),
overlap,
2 * pxp.N,
100,
200,
e_diff=0.5)
plt.scatter(H.sector.eigvalues(k), overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(H.sector.eigvalues(k)[scar_indices[n]],
overlap[scar_indices[n]],
marker="x",
color="red",
s=100)
plt.show()
#redifine su3_basis as the ritz vectors (new linear combs)
H_fsa = np.dot(np.conj(np.transpose(su3_basis)),
np.dot(H.sector.matrix(k), su3_basis))
e, u = np.linalg.eigh(H_fsa)
su3_basis = np.dot(su3_basis, u)
#find 2N+1 basis states with largest overlap with scars states
max_scar_overlap = np.zeros(np.size(su3_basis, axis=1))
for n in range(0, np.size(max_scar_overlap, axis=0)):
scarOverlap = np.zeros(np.size(scar_indices))
for m in range(0, np.size(scarOverlap, axis=0)):
scarOverlap[m] = np.vdot(
su3_basis[:, n],
H.sector.eigvectors(k)[:, scar_indices[m]])
max_scar_overlap[n] = np.max(scarOverlap)
su3_indices = np.arange(0, np.size(su3_basis, axis=1))
max_scar_overlap, su3_indices = (list(t) for t in zip(
*sorted(zip(max_scar_overlap, su3_indices))))
max_scar_overlap = np.flip(max_scar_overlap)
su3_indices = np.flip(su3_indices)
su3_sub_indices = su3_indices[:np.size(scar_indices)]
su3_sub_basis = np.zeros(np.size(su3_basis, axis=0))
for n in range(0, np.size(su3_sub_indices, axis=0)):
su3_sub_basis = np.vstack(
(su3_sub_basis, su3_basis[:, su3_sub_indices[n]]))
su3_sub_basis = np.transpose(np.delete(su3_sub_basis, 0, axis=0))
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)))
print(coef, subspace_variance)
e, u = np.linalg.eigh(H_fsa)
H2 = np.dot(H.sector.matrix(k), H.sector.matrix(k))
H2_fsa = np.dot(np.conj(np.transpose(su3_sub_basis)),
np.dot(H2, su3_sub_basis))
H_fsa = np.dot(np.conj(np.transpose(su3_sub_basis)),
np.dot(H.sector.matrix(k), su3_sub_basis))
subspace_variance = np.real(np.trace(H2_fsa - np.dot(H_fsa, H_fsa)))
print(coef, subspace_variance)
e, u = np.linalg.eigh(H_fsa)
return subspace_variance / np.size(su3_sub_basis, axis=1)
H_fsa = np.dot(np.conj(np.transpose(fsa_basis)),
np.dot(H.sector.matrix(), fsa_basis))
Hz_fsa = np.dot(np.conj(np.transpose(fsa_basis)), np.dot(Hz, fsa_basis))
print(np.diag(Hz_fsa))
print(Hz_fsa[1, 1] - Hz_fsa[0, 0])
plt.matshow(np.abs(H_fsa))
plt.show()
plt.matshow(np.abs(Hz_fsa))
plt.show()
overlap = eig_overlap(z, H).eval()
scar_indices = np.unique(
np.sort(get_top_band_indices(H.sector.eigvalues(), overlap, pxp.N)))
plt.scatter(H.sector.eigvalues(), overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(H.sector.eigvalues()[scar_indices[n]],
overlap[scar_indices[n]],
marker="x",
color="red",
s=100)
plt.show()
Z_eff = np.zeros((np.size(scar_indices), np.size(scar_indices)))
for n in range(0, np.size(scar_indices, axis=0)):
Z_eff[n, n] = H.sector.eigvalues()[scar_indices[n]]
# print(np.sort(np.diag(Z_eff)))
# print(Z_eff[1,1]-Z_eff[0,0])
V.site_ops[1] = np.array([[0, 1], [1, 0]])
V.model = np.array([[0, 1, 1, 1, 0]])
V.model_coef = np.array([1])
# V.model = np.array([[0,1,0,0],[0,0,1,0]])
# V.model_coef = np.array([1,1])
H0.gen()
V.gen()
z = zm_state(2, 1, pxp)
#get scar z2 overlap (no pert)
H0.sector.find_eig()
overlap = eig_overlap(z, H0).eval()
from Calculations import get_top_band_indices
scar_indices = get_top_band_indices(H0.sector.eigvalues(), overlap, pxp.N, 200,
150, 0.8)
#check got right scars
plt.scatter(H0.sector.eigvalues(), overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(H0.sector.eigvalues()[scar_indices[n]],
overlap[scar_indices[n]],
marker="x",
color="red",
s=100)
plt.show()
scar_overlap = np.zeros(np.size(scar_indices))
for n in range(0, np.size(scar_indices, axis=0)):
scar_overlap[n] = overlap[scar_indices[n]]
N = 18
pxp = unlocking_System([0],"periodic",2,N)
pxp.gen_basis()
e_nopert = np.load("./pxp,no_pert,e,18.npy")
u_nopert = np.load("./pxp,no_pert,u,18.npy")
e_pert = np.load("./pxp,pert,e,18.npy")
u_pert = np.load("./pxp,pert,u,18.npy")
z=zm_state(3,1,pxp)
overlap_pert = np.log10(np.abs(u_pert[pxp.keys[z.ref],:])**2)
overlap_nopert = np.log10(np.abs(u_nopert[pxp.keys[z.ref],:])**2)
from Calculations import get_top_band_indices
scar_indices_pert = get_top_band_indices(e_pert,overlap_pert,int(2*N/3),150,400,e_diff = 0.5)
scar_indices_nopert = get_top_band_indices(e_nopert,overlap_nopert,int(2*N/3),150,400,e_diff = 0.5)
plt.scatter(e_pert,overlap_pert)
for n in range(0,np.size(scar_indices_pert,axis=0)):
plt.scatter(e_pert[scar_indices_pert[n]],overlap_pert[scar_indices_pert[n]],marker="x",s=100,color="red")
plt.show()
plt.scatter(e_nopert,overlap_nopert)
for n in range(0,np.size(scar_indices_nopert,axis=0)):
plt.scatter(e_nopert[scar_indices_nopert[n]],overlap_nopert[scar_indices_nopert[n]],marker="x",s=100,color="red")
plt.show()
M = np.zeros((np.size(scar_indices_nopert,axis=0),np.size(scar_indices_pert,axis=0)),dtype=complex)
for n in range(0,np.size(scar_indices_pert,axis=0)):
for m in range(0,np.size(scar_indices_nopert,axis=0)):
z = zm_state(2, 1, pxp)
k = pxp_syms.find_k_ref(z.ref)
H = spin_Hamiltonian(pxp, "x", pxp_syms)
overlapSectors = dict()
for n in range(0, np.size(k, axis=0)):
H.gen(k[n])
H.sector.find_eig(k[n])
overlapSectors[n] = eig_overlap(z, H, k[n]).eval()
overlap = np.append(overlapSectors[0], overlapSectors[1])
energy = np.append(H.sector.eigvalues(k[0]), H.sector.eigvalues(k[1]))
plt.scatter(energy, overlap)
from Calculations import get_top_band_indices
scar_indices = get_top_band_indices(energy, overlap, N, 100, 200, e_diff=0.5)
scar_e = np.zeros(np.size(scar_indices))
scar_overlap = np.zeros(np.size(scar_indices))
for n in range(0, np.size(scar_indices, axis=0)):
scar_e[n] = energy[scar_indices[n]]
scar_overlap[n] = overlap[scar_indices[n]]
plt.scatter(scar_e, scar_overlap, marker="x", color="red", s=300)
plt.xlabel(r"$E$")
plt.ylabel(r"$\log(\vert \langle Z_2 \vert E \rangle \vert^2)$")
plt.show()
t = np.arange(0, 20, 0.01)
f = fidelity(z, H, "use sym").eval(t, z)
plt.plot(t, f)
plt.xlabel(r"$t$")
plt.ylabel(r"$\vert \langle \psi(0) \vert \psi(t) \rangle \vert^2$")
fsa_overlap = np.log10(np.abs(u[0, :])**2)
fsa_energy = e
plt.scatter(exact_energy, exact_overlap)
plt.scatter(fsa_energy, fsa_overlap, marker="x", color="red", s=100)
plt.show()
t = np.arange(0, 20, 0.01)
f = fidelity(z, H).eval(t, z)
plt.plot(t, f)
plt.show()
#identify scar states for entropy highlight
scar_indices = get_top_band_indices(H.sector.eigvalues(),
exact_overlap,
int(pxp.N / 2),
200,
200,
e_diff=0.5)
#check identified right states
plt.scatter(exact_energy, exact_overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(exact_energy[scar_indices[n]],
exact_overlap[scar_indices[n]],
marker="D",
color="green",
alpha=0.5,
s=100)
plt.show()
#entropy
ent_vals = np.zeros(pxp.dim)
exact_overlap = eig_overlap(z, H).eval()
exact_energy = H.sector.eigvalues()
e, u = np.linalg.eigh(H_fsa)
fsa_overlap = np.log10(np.abs(u[0, :])**2)
fsa_energy = e
#overlap
plt.scatter(exact_energy, exact_overlap)
plt.scatter(fsa_energy, fsa_overlap, marker="x", color="red", s=100)
plt.show()
#identify scar states for entropy highlight
scar_indices = get_top_band_indices(H.sector.eigvalues(),
exact_overlap,
pxp.N,
100,
100,
e_diff=0.5)
#check identified right states
plt.scatter(exact_energy, exact_overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(exact_energy[scar_indices[n]],
exact_overlap[scar_indices[n]],
marker="D",
color="green",
alpha=0.5,
s=100)
plt.show()
#fidelity
t = np.arange(0, 20, 0.01)
Hp.model = np.array([[0, 2, 0], [0, 1, 0], [0, 1, 0]])
Hp.model_coef = np.array([1, 1, 1])
Hp.uc_size = np.array([3, 3, 3])
Hp.uc_pos = np.array([2, 0, 1])
Hp.gen()
Hm = Hp.herm_conj()
H = H_operations.add(Hp, Hm, np.array([1, 1]))
z = zm_state(3, 1, pxp)
H.sector.find_eig()
overlap = eig_overlap(z, H).eval()
from Calculations import get_top_band_indices
scar_indices = get_top_band_indices(H.sector.eigvalues(),
overlap,
int(2 * pxp.N / 3),
100,
200,
e_diff=0.5)
plt.scatter(H.sector.eigvalues(), overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(H.sector.eigvalues()[scar_indices[n]],
overlap[scar_indices[n]],
marker="x",
color="red",
s=100)
plt.show()
ent_vals = np.zeros(pxp.dim)
ent = entropy(pxp)
pbar = ProgressBar()
V1.gen()
V2.gen()
H1 = H_operations.add(H0, V1, np.array([1, 0.108]))
H2 = H_operations.add(H0, V2, np.array([1, 0.122]))
H1.sector.find_eig()
H2.sector.find_eig()
z = zm_state(2, 1, pxp)
overlap1 = eig_overlap(z, H1).eval()
overlap2 = eig_overlap(z, H1).eval()
from Calculations import get_top_band_indices
scar_indices_ppxp = get_top_band_indices(H1.sector.eigvalues(),
overlap1,
pxp.N,
150,
300,
e_diff=0.5)
scar_indices_pxxxp = get_top_band_indices(H2.sector.eigvalues(),
overlap2,
pxp.N,
150,
300,
e_diff=0.5)
plt.scatter(H1.sector.eigvalues(), overlap1)
for n in range(0, np.size(scar_indices_ppxp, axis=0)):
plt.scatter(H1.sector.eigvalues()[scar_indices_ppxp[n]],
overlap1[scar_indices_ppxp[n]],
marker="x",
color="red")
pxp_syms = model_sym_data(pxp, [translational(pxp)])
z = zm_state(2, 1, pxp)
k = pxp_syms.find_k_ref(z.ref)
H = spin_Hamiltonian(pxp, "x")
H.gen()
H.sector.find_eig()
overlap = eig_overlap(z, H).eval()
plt.scatter(H.sector.eigvalues(), overlap)
from Calculations import get_top_band_indices
scar_indices = get_top_band_indices(H.sector.eigvalues(),
overlap,
N,
100,
200,
e_diff=0.5)
scar_e = np.zeros(np.size(scar_indices))
scar_overlap = np.zeros(np.size(scar_indices))
for n in range(0, np.size(scar_indices, axis=0)):
scar_e[n] = H.sector.eigvalues()[scar_indices[n]]
scar_overlap[n] = overlap[scar_indices[n]]
plt.scatter(scar_e, scar_overlap, marker="x", color="red", s=300)
plt.ylim(bottom=-10)
plt.show()
# z=bin_state([1,1,0,1,1,0,1,1,0,1,1,0],pxp)
fidelity(z, H).plot(np.arange(0, 20, 0.01), z)
plt.show()
# if overlap_total[n] <-10:
# to_del = np.append(to_del,n)
# for n in range(np.size(to_del,axis=0)-1,-1,-1):
# overlap_total=np.delete(overlap_total,to_del[n])
# e=np.delete(e,to_del[n])
# np.save("e_temp",e)
# np.save("overlap_temp",overlap_total)
e = np.load("./e_temp.npy")
overlap_total = np.load("./overlap_temp.npy")
e, overlap_total = (list(t) for t in zip(*sorted(zip(e, overlap_total))))
plt.scatter(e, overlap_total)
from Calculations import get_top_band_indices
scar_indices = np.sort(
get_top_band_indices(e, overlap_total, pxp.N + 2, 350, 400, e_diff=1))
scar_indices = np.append(scar_indices, 1)
scar_indices = np.append(scar_indices, np.size(e) - 2)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(e[scar_indices[n]],
overlap_total[scar_indices[n]],
marker="x",
color="red",
s=100)
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]]
scar_e = np.sort(scar_e)
-c * pert_coef[1], -c * pert_coef[2], -c * pert_coef[2], -c * pert_coef[3],
-c * pert_coef[3]
])
# H.model = np.array([[0,1,0],[0,1,0,2],[2,0,1,0]])
# H.model_coef = np.array([c,-c*pert_coef[0],-c*pert_coef[0]])
H.gen()
H.sector.find_eig()
z = zm_state(2, 1, pxp)
fidelity(z, H).plot(np.arange(0, 20, 0.01), z)
plt.show()
overlap = eig_overlap(z, H).eval()
from Calculations import get_top_band_indices
scar_indices = np.sort(
np.unique(get_top_band_indices(H.sector.eigvalues(), overlap, N)))
scar_basis = np.zeros((pxp.dim, np.size(scar_indices)))
for n in range(0, np.size(scar_indices, axis=0)):
scar_basis[scar_indices[n], n] = 1
plt.scatter(H.sector.eigvalues(), overlap)
for n in range(0, np.size(scar_indices, axis=0)):
plt.scatter(H.sector.eigvalues()[scar_indices[n]],
overlap[scar_indices[n]],
s=100,
marker="x",
color="red")
plt.show()
# H=H_operations.add(H0,V,np.array([c,-c*pert_coef]))
rc('text', usetex=True)
# matplotlib.rcParams['figure.dpi'] = 400
N = 18
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
e = np.load("./pxp,e," + str(pxp.N) + ".npy")
u = np.load("./pxp,u," + str(pxp.N) + ".npy")
z3_overlap = np.load("./pxp,z3_overlap," + str(pxp.N) + ".npy")
mps_overlap = np.load("./pxp,mps_overlap," + str(pxp.N) + ".npy")
from Calculations import get_top_band_indices
z3_scar_indices = get_top_band_indices(e,
z3_overlap,
int(2 * pxp.N / 3),
150,
300,
e_diff=0.5)
mps_scar_indices = get_top_band_indices(e,
mps_overlap,
int(2 * pxp.N / 3),
150,
300,
e_diff=0.5)
plt.scatter(e, z3_overlap)
for n in range(0, np.size(z3_scar_indices, axis=0)):
plt.scatter(e[z3_scar_indices[n]],
z3_overlap[z3_scar_indices[n]],
marker="x",
s=100,
# t=np.arange(0,60,0.01)
# 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
# plt.plot(t,f)
# plt.xlabel(r"$t$")
# plt.ylabel(r"$\vert \langle \psi(0) \vert \psi(t) \rangle \vert^2$")
# plt.title(r"$SU_q(2), q=e^{i * 0.01}, N=$"+str(N))
# plt.show()
psi_energy = np.conj(u[0, :])
overlap = np.log10(np.abs(psi_energy)**2)
plt.scatter(e, overlap)
from Calculations import get_top_band_indices
scars_indices = get_top_band_indices(e, overlap, N, 250, 450, e_diff=0.8)
print(scars_indices)
for n in range(0, np.size(scars_indices, axis=0)):
plt.scatter(e[scars_indices[n]],
overlap[scars_indices[n]],
marker="x",
color="red")
plt.show()
eigenvalues = e
to_del = []
for n in range(0, np.size(overlap, axis=0)):
if overlap[n] < -5:
to_del = np.append(to_del, n)
for n in range(np.size(to_del, axis=0) - 1, -1, -1):
overlap = np.delete(overlap, to_del[n])