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
decomp_ref = []
pbar = ProgressBar()
for n in pbar(range(0, np.size(decompBasis.basis, axis=0))):
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(decompBasis.basis[n], axis=0)):
if decompBasis.basis[n][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()
Hm = Hp.herm_conj()
Hz = 1 / 2 * com(Hp.sector.matrix(), Hm.sector.matrix())
Hx = 1 / 2 * (Hp.sector.matrix() + Hm.sector.matrix())
Hy = 1 / 2j * (Hp.sector.matrix() - Hm.sector.matrix())
C = np.dot(Hx, Hx) + np.dot(Hy, Hy) + np.dot(Hz, Hz)
ec, uc = np.linalg.eigh(C)
for m in range(0, np.size(ec, axis=0)):
if np.abs(var(Hz, uc[:, 0])) < 1e-5:
to_keep = np.vstack((to_keep, uc[:, m]))
decomp_ref = np.append(decomp_ref, decompBasis.basis_refs[n])
to_keep = np.transpose(np.delete(to_keep, 0, axis=0))
#init system N = 18 pxp = unlocking_System([0], "periodic", 2, N) pxp.gen_basis() pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=3), PT(pxp)]) Hp = dict() Hp[0] = Hamiltonian(pxp, pxp_syms) Hp[0].site_ops[1] = np.array([[0, 0], [1, 0]]) Hp[0].site_ops[2] = np.array([[0, 1], [0, 0]]) Hp[0].model = np.array([[0, 2, 0], [0, 1, 0], [0, 1, 0]]) Hp[0].model_coef = np.array([1, 1, 1]) Hp[0].uc_size = np.array([3, 3, 3]) Hp[0].uc_pos = np.array([2, 0, 1]) #1st order # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].model = np.array([[0,0,1,0],[0,1,0,0],[0,2,0,0],[0,0,2,0]]) # Hp[1].model_coef = np.array([1,1,1,1]) # Hp[1].uc_size = np.array([3,3,3,3]) # Hp[1].uc_pos = np.array([2,1,2,1]) # Hp[2] = Hamiltonian(pxp,pxp_syms) # Hp[2].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[2].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[2].model = np.array([[0,1,0,0],[0,0,1,0]]) # Hp[2].model_coef = np.array([1,1])
def com(a, b):
return np.dot(a, b) - np.dot(b, a)
N = 12
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
Hp = Hamiltonian(pxp)
Hp.site_ops[1] = np.array([[0, 0], [1, 0]])
Hp.site_ops[2] = np.array([[0, 1], [0, 0]])
Hp.model = np.array([[0, 1, 0], [0, 2, 0]])
Hp.model_coef = np.array([1, 1])
Hp.uc_size = np.array([2, 2])
Hp.uc_pos = np.array([1, 0])
Hp.gen()
Hp = Hp.sector.matrix()
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(Hp, current_state)
if np.abs(np.vdot(next_state, next_state))**2 > 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:
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)])
Hp = dict()
Hp[0] = Hamiltonian(pxp)
Hp[0].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[0].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[0].model = np.array([[0, 1, 0], [0, 2, 0]])
Hp[0].model_coef = np.array([1, 1])
Hp[0].uc_size = np.array([2, 2])
Hp[0].uc_pos = np.array([1, 0])
#1st order pert
Hp[1] = Hamiltonian(pxp)
Hp[1].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[1].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[1].model = np.array([[0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 2, 0,
0]])
Hp[1].model_coef = np.array([1, 1, 1, 1])
Hp[1].uc_size = np.array([2, 2, 2, 2])
Hp[1].uc_pos = np.array([0, 1, 1, 0])
#2nd order perts
Hp[2] = Hamiltonian(pxp)
Hp[2].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[2].site_ops[2] = np.array([[0, 1], [0, 0]])
return exp(Q2, psi) - exp(Q, psi)**2 N = 10 pxp = unlocking_System([0], "periodic", 3, N) pxp.gen_basis() pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=2), PT(pxp)]) #orig H Ip = Hamiltonian(pxp, pxp_syms) Ip.site_ops[1] = np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]]) Ip.site_ops[2] = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]]) Ip.model = np.array([[0, 1, 0], [0, 2, 0]]) Ip.model_coef = np.array([1, -1]) Ip.uc_size = np.array([2, 2]) Ip.uc_pos = np.array([1, 0]) Im = Hamiltonian(pxp, pxp_syms) Im.site_ops[1] = np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]]) Im.site_ops[2] = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]]) Im.model = np.array([[0, 2, 0], [0, 1, 0]]) Im.model_coef = np.array([1, -1]) Im.uc_size = np.array([2, 2]) Im.uc_pos = np.array([1, 0]) Kp = Hamiltonian(pxp, pxp_syms) Kp.site_ops[1] = np.array([[0, 0, 1], [0, 0, 0], [0, 0, 0]]) Kp.site_ops[2] = np.array([[0, 0, 0], [0, 0, 0], [1, 0, 0]]) Kp.model = np.array([[0, 1, 0], [0, 2, 0]]) Kp.model_coef = np.array([1, -1]) Kp.uc_size = np.array([2, 2])
#init system
N = 14
pxp = unlocking_System([0], "periodic", 3, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=2), PT(pxp)])
#orig H
Ip = dict()
Ip[0] = Hamiltonian(pxp, pxp_syms)
Ip[0].site_ops[1] = np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
Ip[0].site_ops[2] = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]])
Ip[0].model = np.array([[0, 1, 0], [0, 2, 0]])
Ip[0].model_coef = np.array([1, -1])
Ip[0].uc_size = np.array([2, 2])
Ip[0].uc_pos = np.array([1, 0])
Ip[1] = Hamiltonian(pxp, pxp_syms)
Ip[1].site_ops[1] = np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
Ip[1].site_ops[2] = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]])
Ip[1].model = np.array([[0, 2, 0, 0], [0, 0, 2, 0], [0, 1, 0, 0], [0, 0, 1,
0]])
Ip[1].model_coef = np.array([1, 1, -1, -1])
Ip[1].uc_size = np.array([2, 2, 2, 2])
Ip[1].uc_pos = np.array([0, 1, 1, 0])
Ip[2] = Hamiltonian(pxp, pxp_syms)
Ip[2].site_ops[1] = np.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
Ip[2].site_ops[2] = np.array([[0, 0, 0], [1, 0, 0], [0, 0, 0]])
Ip[2].model = np.array([[0, 0, 2, 0, 0], [0, 0, 1, 0, 0]])
Ip[2].model_coef = np.array([1, -1])
return np.dot(a, b) - np.dot(b, a) N = 12 pxp = unlocking_System([0], "periodic", 2, N) pxp.gen_basis() pxp_syms = model_sym_data(pxp, [translational(pxp), parity(pxp)]) Hp = dict() Hp[0] = Hamiltonian(pxp) Hp[0].site_ops[1] = np.array([[0, 0], [1, 0]]) Hp[0].site_ops[2] = np.array([[0, 1], [0, 0]]) Hp[0].model = np.array([[0, 1, 0], [0, 2, 0]]) Hp[0].model_coef = np.array([1, 1]) Hp[0].uc_size = np.array([2, 2]) Hp[0].uc_pos = np.array([1, 0]) Hp[1] = Hamiltonian(pxp) Hp[1].site_ops[1] = np.array([[0, 0], [1, 0]]) Hp[1].site_ops[2] = np.array([[0, 1], [0, 0]]) Hp[1].model = np.array([[0, 2, 1, 2, 0], [0, 1, 2, 1, 0]]) Hp[1].model_coef = np.array([1, 1]) Hp[1].uc_size = np.array([2, 2]) Hp[1].uc_pos = np.array([0, 1]) # Hp[0] = Hamiltonian(pxp) # Hp[0].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[0].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[0].model = np.array([[0,1,0],[0,2,0]]) # Hp[0].model_coef = np.array([1,1]) # Hp[0].uc_size = np.array([2,2])
def com(a,b):
return np.dot(a,b)-np.dot(b,a)
#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])
# matplotlib.rcParams['figure.dpi'] = 400
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]])
pxp.gen_basis() pxp = pxp.U1_sector(5) print(pxp.dim) pxp_syms = model_sym_data(pxp,[translational(pxp),parity(pxp)]) J = 1 Jz = 1 Hp = dict() Hp[0] = Hamiltonian(pxp,pxp_syms) Hp[0].site_ops[1] = np.array([[0,0],[1,0]]) Hp[0].site_ops[2] = np.array([[0,1],[0,0]]) Hp[0].site_ops[3] = np.array([[-1/2,0],[0,1/2]]) Hp[0].model = np.array([[0,2,1,0],[0,1,2,0],[3,3]]) Hp[0].model_coef = np.array([J/2,J/2,Jz/2]) Hp[0].uc_size = np.array([2,2,1]) Hp[0].uc_pos = np.array([1,0,0]) # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].model = np.array([[0,2,1,0,0],[0,0,2,1,0],[0,0,1,2,0],[0,1,2,0,0]]) # Hp[1].model_coef = np.array([1,1,1,1]) # Hp[1].uc_size = np.array([2,2,2,2]) # Hp[1].uc_pos = np.array([1,0,1,0]) # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].site_ops[4] = np.array([[0,0],[0,1]]) # Hp[1].model = np.array([[0,4,0,1,2,0],[0,1,2,0,4,0],[0,2,1,0,4,0],[0,4,0,2,1,0]]) # Hp[1].model_coef = np.array([1,1,1,1])
#init system N=20 pxp = unlocking_System([0],"periodic",2,N) pxp.gen_basis() pxp_syms = model_sym_data(pxp,[translational_general(pxp,order=4),PT(pxp)]) Hp = dict() Hp[0] = Hamiltonian(pxp,pxp_syms) Hp[0].site_ops[1] = np.array([[0,0],[1,0]]) Hp[0].site_ops[2] = np.array([[0,1],[0,0]]) Hp[0].model = np.array([[0,1,2,1,0],[0,2,1,2,0],[0,2,1,2,0],[0,1,2,1,0]]) Hp[0].model_coef = np.array([1,1,1,1]) Hp[0].uc_size = np.array([4,4,4,4]) Hp[0].uc_pos = np.array([2,3,0,1]) # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].site_ops[4] = np.array([[0,0],[0,1]]) # Hp[1].model = np.array([[0,2,1,0,4,0,0],[0,0,4,0,1,2,1,0],[0,0,4,0,2,1,2,0],[0,1,2,1,0,4,0,0]]) # Hp[1].model_coef = np.array([1,1,1,1]) # Hp[1].uc_size = np.array([4,4,4,4]) # Hp[1].uc_pos = np.array([0,2,0,2]) # Hp[1].gen() Hp[1] = Hamiltonian(pxp,pxp_syms) Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) Hp[1].site_ops[4] = np.array([[0,0],[0,1]])
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)])
Hp = dict()
Hp[0] = Hamiltonian(pxp,pxp_syms)
Hp[0].site_ops[1] = np.array([[0,0],[1,0]])
Hp[0].site_ops[2] = np.array([[0,1],[0,0]])
Hp[0].model = np.array([[0,2,0],[0,1,0],[0,1,0],[0,1,0]])
Hp[0].model_coef = np.array([1,1,1,1])
Hp[0].uc_size = np.array([4,4,4,4])
Hp[0].uc_pos = np.array([3,0,1,2])
Hp[1] = Hamiltonian(pxp,pxp_syms)
Hp[1].site_ops[1] = np.array([[0,0],[1,0]])
Hp[1].site_ops[2] = np.array([[0,1],[0,0]])
Hp[1].model = np.array([[0,2,1,2,0],[0,2,1,2,0]])
Hp[1].model_coef = np.array([1,1])
Hp[1].uc_size = np.array([4,4])
Hp[1].uc_pos = np.array([3,1])
z=zm_state(4,1,pxp)
for n in range(0,len(Hp)):
Hp[n].gen()
Hp_total = H_operations.add(Hp[0],Hp[1], np.array([1,-1]))
H = H_operations.add(Hp_total,Hp_total.herm_conj(),np.array([1,1]))
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational(pxp), parity(pxp)])
H0 = Hamiltonian(pxp)
H0.site_ops[1] = np.array([[0, 1], [1, 0]])
H0.model = np.array([[0, 1, 1, 1, 0]])
H0.model_coef = np.array([1])
V = Hamiltonian(pxp)
V.site_ops[1] = np.array([[0, 1], [1, 0]])
V.site_ops[4] = np.array([[0, 0], [0, 1]])
V.model = np.array([[0, 1, 1, 1, 0, 4, 0], [0, 4, 0, 1, 1, 1, 0],
[0, 1, 1, 1, 0, 4, 0], [0, 4, 0, 1, 1, 1, 0]])
V.model_coef = np.array([1, 1, 1, 1])
V.uc_size = np.array([4, 4, 4, 4])
V.uc_pos = np.array([2, 0, 0, 2])
def fidelity_eval(psi_energy, e, t):
evolved_state = time_evolve_state(psi_energy, e, t)
f = np.abs(np.vdot(evolved_state, psi_energy))**2
return -f
from copy import deepcopy
from Hamiltonian_Classes import H_operations
from scipy.optimize import minimize, minimize_scalar
def fidelity_error(coef, plot=False):
coef = coef[0]
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)])
Hp = dict()
Hp[0] = Hamiltonian(pxp)
Hp[0].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[0].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[0].model = np.array([[0, 1, 0], [0, 2, 0]])
Hp[0].model_coef = np.array([1, 1])
Hp[0].uc_size = np.array([2, 2])
Hp[0].uc_pos = np.array([1, 0])
#1st order pert
Hp[1] = Hamiltonian(pxp)
Hp[1].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[1].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[1].model = np.array([[0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 2, 0,
0]])
Hp[1].model_coef = np.array([1, 1, 1, 1])
Hp[1].uc_size = np.array([2, 2, 2, 2])
Hp[1].uc_pos = np.array([0, 1, 1, 0])
#2nd order perts
Hp[2] = Hamiltonian(pxp)
Hp[2].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[2].site_ops[2] = np.array([[0, 1], [0, 0]])
#init system N=20 pxp = unlocking_System([0],"periodic",2,N) pxp.gen_basis() pxp_syms = model_sym_data(pxp,[translational_general(pxp,order=4),PT(pxp)]) Hp = dict() Hp[0] = Hamiltonian(pxp,pxp_syms) Hp[0].site_ops[1] = np.array([[0,0],[1,0]]) Hp[0].site_ops[2] = np.array([[0,1],[0,0]]) Hp[0].model = np.array([[0,1,2,1,0],[0,1,2,1,0],[0,2,1,2,0],[0,1,2,1,0]]) Hp[0].model_coef = np.array([1,1,1,1]) Hp[0].uc_size = np.array([4,4,4,4]) Hp[0].uc_pos = np.array([2,3,0,1]) # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].site_ops[4] = np.array([[0,0],[0,1]]) # Hp[1].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[1].model_coef = np.array([1,1,1,1]) # Hp[1].uc_size = np.array([4,4,4,4]) # Hp[1].uc_pos = np.array([1,3,3,1]) # Hp[2] = Hamiltonian(pxp,pxp_syms) # Hp[2].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[2].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[2].site_ops[4] = np.array([[0,0],[0,1]]) # Hp[2].model = np.array([[0,1,2,1,0,4,0,0],[0,1,2,1,0,4,0,0],[0,0,4,0,1,2,1,0],[0,0,4,0,1,2,1,0]])
#init system
N = 9
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
pxp_syms = model_sym_data(pxp, [translational_general(pxp, order=3)])
Hp = dict()
Hp[0] = Hamiltonian(pxp, pxp_syms)
Hp[0].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[0].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[0].model = np.array([[0, 2, 0], [0, 1, 0], [0, 1, 0]])
Hp[0].model_coef = np.array([1, 1, 1])
Hp[0].uc_size = np.array([3, 3, 3])
Hp[0].uc_pos = np.array([2, 0, 1])
#1st order
Hp[1] = Hamiltonian(pxp, pxp_syms)
Hp[1].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[1].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[1].model = np.array([[0, 0, 1, 0], [0, 1, 0, 0], [0, 2, 0, 0], [0, 0, 2,
0]])
Hp[1].model_coef = np.array([1, 1, 1, 1])
Hp[1].uc_size = np.array([3, 3, 3, 3])
Hp[1].uc_pos = np.array([2, 1, 2, 1])
Hp[2] = Hamiltonian(pxp, pxp_syms)
Hp[2].site_ops[1] = np.array([[0, 0], [1, 0]])
Hp[2].site_ops[2] = np.array([[0, 1], [0, 0]])
Hp[2].model = np.array([[0, 1, 0, 0], [0, 0, 1, 0]])
#init system
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)])
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([[0, 1, 2, 1, 0], [0, 2, 1, 2, 0], [0, 2, 1, 2, 0],
[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([2, 3, 0, 1])
# 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])
#init system N=16 pxp = unlocking_System([0],"periodic",2,N) pxp.gen_basis() pxp_syms = model_sym_data(pxp,[translational_general(pxp,order=4)]) # pxp_syms = model_sym_data(pxp,[translational(pxp)]) Hp = dict() Hp[0] = Hamiltonian(pxp,pxp_syms) Hp[0].site_ops[1] = np.array([[0,0],[1,0]]) Hp[0].site_ops[2] = np.array([[0,1],[0,0]]) Hp[0].model = np.array([[0,2,0],[0,1,0],[0,1,0],[0,1,0]]) Hp[0].model_coef = np.array([1,1,1,1]) Hp[0].uc_size = np.array([4,4,4,4]) Hp[0].uc_pos = np.array([3,0,1,2]) # Hp[1] = Hamiltonian(pxp,pxp_syms) # Hp[1].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[1].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[1].model = np.array([[0,1,2,1,0]]) # Hp[1].model_coef = np.array([1]) # Hp[1].uc_size = np.array([4]) # Hp[1].uc_pos = np.array([0]) # Hp[2] = Hamiltonian(pxp,pxp_syms) # Hp[2].site_ops[1] = np.array([[0,0],[1,0]]) # Hp[2].site_ops[2] = np.array([[0,1],[0,0]]) # Hp[2].model = np.array([[0,2,1,2,0],[0,2,1,2,0]]) # Hp[2].model_coef = np.array([1,1]) # Hp[2].uc_size = np.array([4,4])
N = 21
pxp = unlocking_System([0], "periodic", 2, N)
pxp.gen_basis()
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")
pxxxp_config = model_space.basis[indices[1][index_row_loc[count]]] print(pxp_config, pxxxp_config) # print(index_spacing_error[count]) # print(index_var_error[count]) Hp = gen_Hp(pxp_config, pxxxp_config) Hm = np.conj(np.transpose(Hp)) 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)
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()
#init system N=10 pxp = unlocking_System([0],"periodic",3,N) pxp.gen_basis() pxp_syms = model_sym_data(pxp,[translational_general(pxp,order=2),PT(pxp)]) #orig H Ip = dict() Ip[0] = Hamiltonian(pxp,pxp_syms) Ip[0].site_ops[1] = np.array([[0,1,0],[0,0,0],[0,0,0]]) Ip[0].site_ops[2] = np.array([[0,0,0],[1,0,0],[0,0,0]]) Ip[0].model = np.array([[0,1,0],[0,2,0]]) Ip[0].model_coef = np.array([1,-1]) Ip[0].uc_size = np.array([2,2]) Ip[0].uc_pos = np.array([1,0]) Ip[1] = Hamiltonian(pxp,pxp_syms) Ip[1].site_ops[1] = np.array([[0,1,0],[0,0,0],[0,0,0]]) Ip[1].site_ops[2] = np.array([[0,0,0],[1,0,0],[0,0,0]]) Ip[1].model = np.array([[0,2,0,0],[0,0,2,0],[0,1,0,0],[0,0,1,0]]) Ip[1].model_coef = np.array([1,1,-1,-1]) Ip[1].uc_size = np.array([2,2,2,2]) Ip[1].uc_pos = np.array([0,1,1,0]) Im = dict() Im[0] = Hamiltonian(pxp,pxp_syms) Im[0].site_ops[1] = np.array([[0,1,0],[0,0,0],[0,0,0]]) Im[0].site_ops[2] = np.array([[0,0,0],[1,0,0],[0,0,0]]) Im[0].model = np.array([[0,2,0],[0,1,0]]) Im[0].model_coef = np.array([1,-1])
