def xx_2site(self):
pxp = unlocking_System(np.arange(0, self.base), "open", self.base, 2)
pxp.gen_basis()
H = Hamiltonian(pxp)
H.site_ops[1] = np.array([[0, 1], [1, 0]])
H.model = np.array([[1, 1]])
H.model_coef = np.array([[1]])
H.gen()
H.sector.find_eig()
return H
def pxp_3site(self, Nc):
pxp = unlocking_System(np.arange(0, self.base), "open", self.base, 3)
pxp.gen_basis()
X = spin_Hamiltonian(pxp, "x").site_ops[1]
H = Hamiltonian(pxp)
H.site_ops[1] = X
H.model = np.array([[0, 1, 0]])
H.model_coef = np.array([[1]])
H.gen()
H.sector.find_eig()
return H
def HpFromKey(key):
Hp = Hamiltonian(pxp)
Hp.site_ops[1] = np.array([[0, 0], [1, 0]])
Hp.site_ops[2] = np.array([[0, 1], [0, 0]])
model = []
for m in range(0, np.size(key, axis=0)):
if key[m] == 1:
model.append([0, 1, 0])
else:
model.append([0, 2, 0])
Hp.model = model
Hp.model_coef = np.ones(pxp.N)
Hp.uc_size = pxp.N * np.ones(pxp.N)
Hp.uc_pos = np.arange(0, pxp.N)
Hp.gen()
return Hp
def cost(alpha):
H=Hamiltonian(pxp_half,"x")
H.site_ops[1] = np.array([[0,alpha[0]],[alpha[0],0]])
H.model = np.array([[1]])
H.model_coef=np.array((1))
H.gen()
H.sector.find_eig()
z_rydberg = zm_state(2,1,pxp_half)
f_neel_ham = fidelity(z_rydberg,H).eval(t,z_rydberg)
# plt.plot(t,f_neel_ham)
# plt.show()
cut_index = 5
for n in range(0,np.size(f_neel_ham,axis=0)):
if f_neel_ham[n]<0.1:
cut_index = n
break
max_index = np.argmax(f_neel_ham[cut_index:])
t0_ham = t[max_index]
print(cost,t0_ham)
return np.abs(t0_ham-t0_floquet)
H.gen() H.sector.find_eig() z=zm_state(2,1,pxp) #krylov basis krylov_dim = 2*pxp.N krylov_basis = gen_krylov_basis(H.sector.matrix(),krylov_dim,z.prod_basis(),pxp,orth="qr") #FSA basis # P+P on even sites Ipe = Hamiltonian(pxp,pxp_syms) Ipe.site_ops[1] = np.array([[0,1,0],[0,0,0],[0,0,0]]) Ipe.model = np.array([[0,1,0]]) Ipe.model_coef = np.array([1]) Ipe.gen(parity=1) Imo = Hamiltonian(pxp,pxp_syms) Imo.site_ops[1] = np.array([[0,0,0],[1,0,0],[0,0,0]]) Imo.model = np.array([[0,1,0]]) Imo.model_coef = np.array([1]) Imo.gen(parity=0) Ip = H_operations.add(Ipe,Imo,np.array([1,-1])) Ip = Ip.sector.matrix() Im = np.conj(np.transpose(Ip)) plt.matshow(np.abs(Ip)) plt.show() Kpe = Hamiltonian(pxp,pxp_syms) Kpe.site_ops[1] = np.array([[0,0,1],[0,0,0],[0,0,0]]) Kpe.model = np.array([[0,1,0]]) Kpe.model_coef = np.array([1])
def exp(Q, psi):
return np.vdot(psi, np.dot(Q, psi))
def var(Q, psi):
Q2 = np.dot(Q, Q)
return exp(Q2, psi) - exp(Q, psi)**2
N = 12
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=4), PT(pxp)])
H = Hamiltonian(pxp, pxp_syms)
H.site_ops[1] = np.array([[0, 1], [1, 0]])
H.model = np.array([[0, 1, 0], [0, 1, 1, 1, 0], [0, 1, 1, 1, 0]])
H.model_coef = np.array([1, -1, -1])
H.uc_size = np.array([1, 4, 4])
H.uc_pos = np.array([0, 3, 1])
H.gen()
H.sector.find_eig()
z = zm_state(4, 1, pxp)
eig_overlap(z, H).plot()
plt.show()
fidelity(z, H).plot(np.arange(0, 20, 0.01), z)
plt.show()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=3)])
H0 = Hamiltonian(pxp, pxp_syms)
H0.site_ops[1] = np.array([[0, 1], [1, 0]])
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]]])
# Hp = Hamiltonian(pxp,pxp_syms)
# Hp.site_ops[1] = np.array([[0,0],[1,0]])
# Hp.site_ops[2] = np.array([[0,1],[0,0]])
# Hp.site_ops[4] = np.array([[0,0],[0,1]])
# Hp.model = np.array([[0,1,2,1,0,4,0],[0,1,2,1,0,4,0],[0,4,0,1,2,1,0],[0,4,0,1,2,1,0]])
# Hp.model_coef = np.array([1,1,1,1])
# Hp.uc_size = np.array([4,4,4,4])
# Hp.uc_pos = np.array([1,3,3,1])
z = zm_state(4, 1, pxp)
k = pxp_syms.find_k_ref(z.ref)
print(k)
# for n in range(0,np.size(k,axis=0)):
# Hp.gen(k[n])
Hp.gen()
Hm = Hp.herm_conj()
# Hz = 1/2 * com(Hp.sector.matrix(k[0]),Hm.sector.matrix(k[0]))
Hz = 1 / 2 * com(Hp.sector.matrix(), Hm.sector.matrix())
plt.matshow(np.abs(Hz))
plt.show()
e, u = np.linalg.eigh(Hz)
print(e)
from Diagnostics import print_wf
print_wf(u[:, 0], pxp, 1e-2)
print("\n")
print_wf(u[:, 1], pxp, 1e-2)
print("\n")
print_wf(u[:, 2], pxp, 1e-2)
print("\n")
print_wf(u[:, 3], pxp, 1e-2)
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
H0.gen()
V.gen()
from scipy.optimize import minimize
res = minimize(lambda coef: fidelity_error(coef), method="Nelder-Mead", x0=[0])
fidelity_error([res.x], plot=True)
#krylov basis
krylov_dim = 2 * pxp.N
krylov_basis = gen_krylov_basis(H.sector.matrix(),
krylov_dim,
z.prod_basis(),
pxp,
orth="qr")
#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)
Hp_test0 = Hamiltonian(pxp)
Hp_test0.site_ops[1] = np.array([[0, 0], [1, 0]])
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
d = np.size(temp)-1
if d > int(N/2):
d = N - d
model_coef = np.append(model_coef,J/np.power(d,alpha))
model.append(temp)
Hz = Hamiltonian(pxp,pxp_syms)
Hz.site_ops[1] = np.array([[-1,0],[0,1]])
Hz.model = model
Hz.model_coef = model_coef
Hx = Hamiltonian(pxp,pxp_syms)
Hx.site_ops[1] = np.array([[0,1],[1,0]])
Hx.model = np.array([[1]])
Hx.model_coef = np.array([-B])
k=[0]
z=ref_state(np.max(pxp.basis_refs),pxp)
Hz.gen(k)
Hx.gen(k)
H = H_operations.add(Hz,Hx,np.array([1,1]))
H.sector.find_eig(k)
overlap = eig_overlap(z,H,k).eval()
plt.scatter(H.sector.eigvalues(k),overlap)
plt.title(r"$H = -\sum_{i<j}^L \frac{J}{r_{ij}^\alpha} \sigma_i^z \sigma_{i+1}^z - B \sum_i \sigma_i^x$"+"\n"+r"$J=1$, $B=0.27$, $\alpha=2.3$, $k=0$, $N=$"+str(pxp.N))
plt.ylabel(r"$\log(\vert \langle 1111... \vert E \rangle \vert^2)$")
plt.xlabel(r"$E$")
plt.show()
#init system N = 20 pxp = unlocking_System([0], "periodic", 2, N) pxp.gen_basis() # pxp_syms = model_sym_data(pxp,[translational_general(pxp,order=2),PT(pxp)]) pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=2), PT(pxp)]) z = zm_state(4, 1, pxp) k = pxp_syms.find_k_ref(z.ref) H = Hamiltonian(pxp, pxp_syms) H.site_ops[1] = np.array([[0, 1], [1, 0]]) H.model = np.array([[0, 1, 1, 1, 0]]) H.model_coef = np.array([1]) H.gen() # from Calculations import gen_krylov_basis # k=[0,0] # H.gen(k) # krylovBasis = gen_krylov_basis(H.sector.matrix(k),pxp.dim,z.sym_basis(k,pxp_syms)) # H_krylov = np.dot(np.conj(np.transpose(krylovBasis)),np.dot(H.sector.matrix(k),krylovBasis)) # e,u = np.linalg.eigh(H_krylov) # ls = level_stats(e) # print(np.shape(H_krylov)) # print(ls.mean()) # krylovBasis = dict() # for n in range(0,np.size(k,axis=0)): # krylovBasis[n] = gen_krylov_basis(H.sector.matrix(k[n]),pxp.dim,z.sym_basis(k[n],pxp_syms))
H = Hamiltonian(pxp, pxp_syms)
H.site_ops[1] = np.array([[0, 1], [1, 0]])
H.site_ops[2] = np.array([[-1, 0], [0, 1]])
H.model = np.array([[0, 1, 0], [0, 1, 0, 2], [2, 0, 1, 0], [2, -1, 0, 1, 0],
[0, 1, 0, -1, 2], [2, -1, -1, 0, 1, 0],
[0, 1, 0, -1, -1, 2], [2, -1, -1, -1, 0, 1, 0],
[0, 1, 0, -1, -1, -1, 2]])
H.model_coef = np.array([
1, -pert_coef[0], -pert_coef[0], -pert_coef[1], -pert_coef[1],
-pert_coef[2], -pert_coef[2], -pert_coef[3], -pert_coef[3]
])
# H.model = np.array([[0,1,0],[0,1,0,2],[2,0,1,0]])
# H.model_coef = np.array([1,-pert_coef[0],-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()
#find rescaling such that E1-E0 = 1
def gap(H, c):
e, u = np.linalg.eigh(c * H)
gap = e[1] - e[0]
return np.abs(1 - gap)
from scipy.optimize import minimize_scalar
pxp_syms = model_sym_data(pxp, [translational(pxp)])
H0 = Hamiltonian(pxp, pxp_syms)
H0.site_ops[1] = np.array([[0, 1], [1, 0]])
H0.model = np.array([[0, 1, 0]])
H0.model_coef = np.array([1])
P = Hamiltonian(pxp, pxp_syms)
P.site_ops[1] = np.array([[0, 1], [1, 0]])
P.site_ops[2] = np.array([[1, 0], [0, 0]])
P.site_ops[3] = np.array([[0, 0], [0, 1]])
P.model = np.array([[2, 1, 3], [3, 1, 2]])
P.model_coef = np.array([1, 1])
k = [0]
H0.gen(k)
P.gen(k)
block_refs = pxp_syms.find_block_refs(k)
block_keys = dict()
for n in range(0, np.size(block_refs, axis=0)):
block_keys[block_refs[n]] = n
V_vals = np.arange(0.01, 3, 0.01)
for count in range(0, np.size(V_vals, axis=0)):
V = V_vals[count]
H = H_operations.add(H0, P, np.array([V, 1]))
H.sector.find_eig(k)
neel = zm_state(2, 1, pxp, 1)
pol = ref_state(0, pxp)
H.gen() H.sector.find_eig() z=zm_state(2,1,pxp) #krylov basis krylov_dim = pxp.N krylov_basis = gen_krylov_basis(H.sector.matrix(),krylov_dim,z.prod_basis(),pxp,orth="qr") #FSA basis # P+P on even sites pe = Hamiltonian(pxp,pxp_syms) pe.site_ops[1] = np.array([[0,1],[0,0]]) pe.model = np.array([[0,1,0],]) pe.model_coef = np.array([1]) pe.gen() #P-P on odd sites mo = Hamiltonian(pxp,pxp_syms) mo.site_ops[1] = np.array([[0,0],[1,0]]) mo.model = np.array([[0,1,0]]) mo.model_coef = np.array([1]) mo.gen() #Raising op # Hp = H_operations.add(pe,mo,np.array([1,1])) # Hp = Hp.sector.matrix() Hp = mo.sector.matrix() Hm = np.conj(np.transpose(Hp)) Hx = Hp + Hm
rc('text', usetex=True)
# matplotlib.rcParams['figure.dpi'] = 400
N = 16
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational(pxp), parity(pxp)])
H0 = spin_Hamiltonian(pxp, "x", pxp_syms)
H0.gen()
Hpe = Hamiltonian(pxp, pxp_syms)
Hpe.site_ops[1] = np.array([[0, 1], [0, 0]])
Hpe.model = np.array([[0, 1, 0]])
Hpe.model_coef = np.array([1])
Hpe.gen(parity=0)
Hpo = Hamiltonian(pxp, pxp_syms)
Hpo.site_ops[1] = np.array([[0, 1], [0, 0]])
Hpo.model = np.array([[0, 1, 0]])
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]])
rc('text', usetex=True)
# matplotlib.rcParams['figure.dpi'] = 400
N = 12
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational(pxp), parity(pxp)])
pert_coef = 0.051
H0 = spin_Hamiltonian(pxp, "x", pxp_syms)
V = Hamiltonian(pxp, pxp_syms)
V.site_ops[1] = np.array([[0, 1], [1, 0]])
V.site_ops[2] = np.array([[-1, 0], [0, 1]])
V.model = np.array([[2, 0, 1, 0], [0, 1, 0, 2]])
V.model_coef = np.array([1, 1])
V.gen()
H0.gen()
H = H_operations.add(H0, V, np.array([1, -pert_coef]))
#find rescaling such that E1-E0 = 1
def gap(H, c):
e, u = np.linalg.eigh(c * H)
gap = e[1] - e[0]
# print(gap,c)
return gap
from scipy.optimize import minimize_scalar
res = minimize_scalar(lambda c: np.abs(gap(H.sector.matrix(), c) - 1),
method="golden",
pxp.gen_basis()
pxp_syms = model_sym_data(pxp,[translational(pxp)])
H = Hamiltonian(pxp,pxp_syms)
H.site_ops[1] = np.array([[0,1],[1,0]])
# H.model = np.array([[0,1,0],[0,1,1,1,0]])
H.model = np.array([[0,1,0],[0,0,1,0],[0,1,0,0]])
# H.model_coef = np.array([1,0.122959959])
a=0.108
H.model_coef = np.array([1,a,a])
z=zm_state(2,1,pxp)
k=pxp_syms.find_k_ref(z.ref)
for n in range(0,np.size(k,axis=0)):
H.gen(k[n])
H.sector.find_eig(k[n])
eig_overlap(z,H,k[n]).plot()
plt.title(r"$H=PXP + \lambda PXXXP$, N="+str(pxp.N))
plt.show()
t=np.arange(0,20,0.001)
f0 = fidelity(z,H,"use sym").eval(t,z)
for n in range(0,np.size(f0,axis=0)):
if f0[n] < 0.1:
cut = n
break
max_index = np.argmax(f0[cut:])
print(t[cut:][max_index])
# plt.plot(t,f0)
#init system N=8 pxp = unlocking_System([0,1],"periodic",2,N) pxp.gen_basis() pxp_syms = model_sym_data(pxp,[translational(pxp)]) Hp = Hamiltonian(pxp,pxp_syms) Hp.site_ops[1] = np.array([[0,0],[1,0]]) Hp.site_ops[2] = np.array([[0,1],[0,0]]) Hp.model = np.array([[1,2],[2,1]]) Hp.model_coef = np.array([1,1]) Hp.uc_size = np.array([2,2]) Hp.uc_pos = np.array([0,1]) Hp.gen() Hm = Hp.herm_conj() Hz = 1/2 * com(Hp.sector.matrix(),Hm.sector.matrix()) lie_algebra_num = com(Hz,Hp.sector.matrix()) Hz_an = Hamiltonian(pxp,pxp_syms) Hz_an.site_ops[1] = np.array([[0,0],[1,0]]) Hz_an.site_ops[2] = np.array([[0,1],[0,0]]) Hz_an.site_ops[3] = np.array([[-1/2,0],[0,1/2]]) Hz_an.site_ops[4] = np.array([[0,0],[0,1]]) Hz_an.model = np.array([[0,4],[4,0],[0,4],[4,0],[1,3,2],[2,3,1],[1,3,2],[2,3,1]]) Hz_an.model_coef = np.array([1/2,1/2,-1/2,-1/2,1,1,-1,-1]) Hz_an.uc_size = np.array([2,2,2,2,2,2,2,2]) Hz_an.uc_pos = np.array([1,0,0,1,1,1,0,0]) Hz_an.gen()
y = 1 / 2j * (Jp - Jm)
z = 1 / 2 * com(Jp, Jm)
z2 = np.dot(z, z)
#create Hamiltonian
J = 1
h = 0.1
D = 0.1
H = Hamiltonian(pxp)
H.site_ops[1] = x
H.site_ops[2] = y
H.site_ops[3] = z
H.site_ops[4] = z2
H.model = np.array([[1, 1], [2, 2], [3], [4]])
H.model_coef = np.array([J, J, h, D])
H.gen()
Hp = np.zeros((pxp.dim, pxp.dim))
for n in range(0, np.size(pxp.basis, axis=0)):
bits = np.copy(pxp.basis[n])
for m in range(0, pxp.N):
if bits[m] == 2:
new_bits = np.copy(bits)
new_bits[m] = 0
new_ref = bin_to_int_base_m(new_bits, pxp.base)
Hp[pxp.keys[new_ref], n] += 2 * (-1)**m
Hm = np.conj(np.transpose(Hp))
Hx = 1 / 2 * (Hp + Hm)
#scarred eigenstates
psi = ref_state(0, pxp).prod_basis()
rc('text', usetex=True)
# matplotlib.rcParams['figure.dpi'] = 400
N = 14
pxp = unlocking_System([0],"periodic",2,N)
pxp.gen_basis()
pxp_syms=model_sym_data(pxp,[translational(pxp),parity(pxp)])
H0=spin_Hamiltonian(pxp,"x",pxp_syms)
H0.gen()
Hp0 = Hamiltonian(pxp,pxp_syms)
Hp0.site_ops[1] = np.array([[0,1],[0,0]])
Hp0.model = np.array([[1]])
Hp0.model_coef = np.array([1])
Hp0.gen()
Hp1 = Hamiltonian(pxp,pxp_syms)
Hp1.site_ops[1] = np.array([[0,1],[0,0]])
Hp1.site_ops[2] = np.array([[0,0],[1,0]])
Hp1.model = np.array([[0,1,2,1,0]])
Hp1.model_coef = np.array([1])
Hp1.gen()
Hm0 = Hamiltonian(pxp,pxp_syms)
Hm0.site_ops[1] = np.array([[0,0],[1,0]])
Hm0.model = np.array([[1]])
Hm0.model_coef = np.array([1])
Hm0.gen()
Hm1 = Hamiltonian(pxp,pxp_syms)
Neel_state_spin_basis = np.zeros(np.size(pxp.basis_refs)) Neel_state_spin_basis[pxp.keys[z.ref]] = 1 Neel_state_clock_basis = np.dot(spin2clock_u, Neel_state_spin_basis) z = zm_state(2, 1, pxp) Neel_state_clock_basis = np.zeros(np.size(pxp.basis_refs)) Neel_state_clock_basis[pxp.keys[z.ref]] = 1 Neel_state_spin_basis = np.dot(clock2spin_u, Neel_state_clock_basis) print(Neel_state_spin_basis) H = Hamiltonian(pxp, pxp_syms) H.site_ops[2] = P_spin_clock_basis H.site_ops[1] = H1.site_ops[1] H.model = np.array(([[2, 1, 2]])) H.model_coef = np.array((1)) H.gen() H.sector.find_eig() print(H.sector.eigvalues()) # eig_overlap.plot(z.bits,H) # plt.show() # fidelity.plot(z.bits,np.arange(0,20,0.01),H) # plt.show() H_clock = Hamiltonian(pxp, pxp_syms) H_clock.site_ops[2] = P H_clock.site_ops[1] = H2.site_ops[1] H_clock.model = np.array([[2, 1, 2]]) H_clock.model_coef = np.array((1)) # H_clock = clock_Hamiltonian(pxp,pxp_syms) H_clock.gen()
N = 15
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=3), PT(pxp)])
z = zm_state(3, 1, pxp)
k = pxp_syms.find_k_ref(z.ref)
V1 = Hamiltonian(pxp, pxp_syms)
V1.site_ops[1] = np.array([[0, 1], [1, 0]])
V1.model = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 1, 0]])
V1.model_coef = np.array([1, 1, 1, 1])
V1.uc_size = np.array([3, 3, 3, 3])
V1.uc_pos = np.array([1, 2, 2, 1])
for n in range(0, np.size(k, axis=0)):
V1.gen(k_vec=k[n])
V2 = Hamiltonian(pxp, pxp_syms)
V2.site_ops[1] = np.array([[0, 1], [1, 0]])
V2.model = np.array([[0, 0, 1, 0], [0, 1, 0, 0]])
V2.model_coef = np.array([1, 1])
V2.uc_size = np.array([3, 3])
V2.uc_pos = np.array([0, 0])
for n in range(0, np.size(k, axis=0)):
V2.gen(k_vec=k[n])
V3 = Hamiltonian(pxp, pxp_syms)
V3.site_ops[1] = np.array([[0, 1], [1, 0]])
V3.model = np.array([[0, 1, 1, 1, 0], [0, 1, 1, 1, 0]])
V3.model_coef = np.array([1, 1])
V3.uc_size = np.array([3, 3])
# print("\n")
# root_refs = find_root_refs(np.array([1,4]),np.array([2,4]),H,sector_refs,from_sector,pxp)
# basis = np.hstack((basis,subcube_basis(root_refs,"Right",6)))
# print("\n")
# root_refs = find_root_refs(np.array([3,0]),np.array([3,3]),H,sector_refs,from_sector,pxp)
# basis = np.hstack((basis,subcube_basis(root_refs,"Left",6)))
# 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)
Hm = Hp1.sector.matrix() + Hp2.sector.matrix()
Hp = np.conj(np.transpose(Hm))
#fsa basis from Neel
z = zm_state(2, 1, pxp)
fsa_basis = z.prod_basis()
current_state = fsa_basis
fsa_dim = pxp.N
for n in range(0, fsa_dim):
new_state = np.dot(Hp, current_state)
H.sector.find_eig()
z=zm_state(2,1,pxp)
#krylov basis
krylov_dim = 2*pxp.N
krylov_basis = gen_krylov_basis(H.sector.matrix(),krylov_dim,z.prod_basis(),pxp,orth="qr")
#FSA basis
# 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)
# Im.gen() # Kp.gen() # Km.gen() # Lp.gen() # Lm.gen() # Ip_pert.gen() # Im_pert.gen() # Kp_pert.gen() # Km_pert.gen() # Lp_pert.gen() # Lm_pert.gen() z = zm_state(2, 1, pxp) # k=pxp_syms.find_k_ref(z.ref) k = [0, 0] 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]))
z = zm_state(2, 1, pxp)
# z=zm_state(3,1,pxp)
# z=ref_state(1,pxp)
hamming_sectors = find_hamming_sectors(z.bits)
hamming_length = 0
for n in range(0, len(hamming_sectors)):
if np.size(hamming_sectors[n]) != 0:
hamming_length = hamming_length + 1
# H=spin_Hamiltonian(pxp,"x")
# H.gen()
V = Hamiltonian(pxp)
V.site_ops[1] = np.array([[0, 0], [0, 1]])
V.model = np.array([[1, 1]])
V.model_coef = np.array([1])
V.gen()
removed_count = np.zeros(len(hamming_sectors))
for n in range(0, len(hamming_sectors)):
c = 0
for m in range(0, np.size(hamming_sectors[n], axis=0)):
ref = hamming_sectors[n][m]
index = pxp.keys[ref]
if V.sector.matrix()[index, index] != 0:
c = c + 1
# c=c+V.sector.matrix()[index,index]
removed_count[n] = c
plt.plot(removed_count)
plt.show()
import scipy as sp import math from Calculations import plot_adjacency_graph N = 12 pxp = unlocking_System([0], "periodic", 2, N) pxp.gen_basis() pxp_syms = model_sym_data(pxp, [translational(pxp)]) H = Hamiltonian(pxp, pxp_syms) H.site_ops[1] = np.array([[0, 0], [1, 0]]) H.site_ops[2] = np.array([[0, 1], [0, 0]]) H.model = np.array([[0, 1, 2, 0], [0, 2, 1, 0]]) H.model_coef = np.array([1, 1]) k = [0] H.gen(k) # H.gen() # H0=spin_Hamiltonian(pxp,"x",pxp_syms) # H0.gen(k) # # H = H_operations.add(H0,H,np.array([1,1/2])) # H = H_operations.add(H0,H,np.array([1,1])) # all states # basis_labels = dict() # for n in range(0,np.size(pxp.basis,axis=0)): # basis_labels[n] = pxp.basis[n] # plot_adjacency_graph(np.abs(H.sector.matrix()),labels=basis_labels) # # plt.title(r"$P^0 X P^1 + P^1 X P^0$, N="+str(pxp.N)) # # plt.title(r"$P^0 X P^1$, N="+str(pxp.N)) # plt.show()
rydberg_subspace[pxp.keys[pxp_half.basis_refs[n]], n] = 1 #pauli ops X = Hamiltonian(pxp, pxp_syms) Y = Hamiltonian(pxp, pxp_syms) Z = Hamiltonian(pxp, pxp_syms) X.site_ops[1] = np.array([[0, 1], [1, 0]]) Y.site_ops[1] = np.array([[0, -1j], [1j, 0]]) Z.site_ops[1] = np.array([[-1, 0], [0, 1]]) X.model, X.model_coef = np.array([[1]]), np.array((1)) Y.model, Y.model_coef = np.array([[1]]), np.array((1)) Z.model, Z.model_coef = np.array([[1]]), np.array((1)) X.gen() Y.gen() Z.gen() #n_i n_i+1 H0 = Hamiltonian(pxp, pxp_syms) H0.site_ops[1] = np.array([[0, 0], [0, 1]]) H0.model = np.array([[1, 1]]) H0.model_coef = np.array((1)) #X_n H_kick = Hamiltonian(pxp, pxp_syms) H_kick.site_ops[1] = np.array([[0, 1], [1, 0]]) H_kick.model = np.array([[1]]) H_kick.model_coef = np.array((1))