def getHamilton(self):
# spin operator
sz = torch.tensor([[1, 0], [0, -1]], dtype=dtype, device=device) / 2
sx = torch.tensor([[0, 1], [1, 0]], dtype=dtype, device=device) / 2
sy = torch.tensor([[0, -1], [1, 0]], dtype=dtype, device=device) / 2
if self.model == "Ising":
H = kron(sz, sz)
elif self.model == "XY":
H = kron(sx, sx) - kron(sy, sy)
return H
def fit_transform(self, X):
N = X.shape[0]
# perform KNN
N = X.shape[0]
pdist = (X[:, None, :] - X[None, :, :]).norm(2, -1)
knn = pdist.topk(self.k, 1, largest=False)[1]
# compute weigths matrix W
W = torch.zeros(N, self.k)
for i in range(N):
Z = X[knn[i]] - kron(torch.ones(self.k, 1), X[i])
C = Z @ Z.t()
C += torch.eye(self.k) * 1e-3 * C.trace()
w = torch.gesv(torch.ones(self.k, 1), C)[0].t()
W[i] = w / w.sum()
# compute Y
M = torch.eye(N)
for i in range(N):
w = W[i:i + 1].t()
ww = w @ w.t()
for k in range(self.k):
M[i, knn[i, k]] -= w[k].item()
M[knn[i, k], i] -= w[k].item()
for l in range(self.k):
M[knn[i, k], knn[i, l]] += ww[k, l]
eigvals, eigvecs = M.eig(True)
indices = eigvals[:, 0].sort()[1][1:self.n_dims + 1]
y = eigvecs[:, indices]
return y
key += '_float32'
cmd = ['mkdir', '-p', key]
subprocess.check_call(cmd)
if args.model == 'J1J2':
#Hamiltonian operators on a bond
sx = torch.tensor([[0, 1], [1, 0]], dtype=dtype, device=device) * 0.5
sy = torch.tensor([[0, -1], [1, 0]], dtype=dtype, device=device) * 0.5
sp = torch.tensor([[0, 1], [0, 0]], dtype=dtype, device=device)
sm = torch.tensor([[0, 0], [1, 0]], dtype=dtype, device=device)
sz = torch.tensor([[1, 0], [0, -1]], dtype=dtype, device=device) * 0.5
id2 = torch.tensor([[1, 0], [0, 1]], dtype=dtype, device=device)
# supply just S.S
Hnn = args.J1 * (
2 * kron(sz, 4 * sx @ sz @ sx) -
(kron(sm, 4 * sx @ sp @ sx) + kron(sp, 4 * sx @ sm @ sx)))
Hnnn = args.J2 * (2 * kron(sz, sz) + (kron(sm, sp) + kron(sp, sm)))
H = torch.cat((Hnn, Hnnn))
Mpx = kron(sx, id2)
Mpy = kron(sy, id2)
Mpz = kron(sz, id2)
else:
print('what model???')
sys.exit(1)
print('Hamiltonian:\n', H)
def closure():
#sx = torch.from_numpy(su2.get_su2_op(""), dtype=dtype, device=device)*0.5
#sy = torch.tensor([[0, -1], [1, 0]], dtype=dtype, device=device)*0.5
sp = torch.from_numpy(su2.get_su2_op(
"sp", dimS)) #, dtype=dtype, device=device)
sm = torch.from_numpy(su2.get_su2_op(
"sm", dimS)) #, dtype=dtype, device=device)
sz = torch.from_numpy(su2.get_su2_op(
"sz", dimS)) #, dtype=dtype, device=device)*0.5
sx = 0.5 * (sp + sm)
sy = 0.5 * (sp - sm)
idop = torch.from_numpy(su2.get_su2_op(
"I", dimS)) #, dtype=dtype, device=device)
rot = torch.from_numpy(su2.get_rot_op(dimS))
# supply just S.S
SS = kron(sz,
rot.t() @ sz @ rot) + 0.5 * (kron(sm,
rot.t() @ sp @ rot) +
kron(sp,
rot.t() @ sm @ rot))
H = (1.0/14.0) * (SS + (7.0/10.0)*SS@SS + (7.0/45.0)*SS@SS@SS \
+ (1.0/90.0)*SS@SS@SS@SS)
D, U = torch.eig(H, eigenvectors=False)
print(D)
Mpx = kron(sx, idop)
Mpy = kron(sy, idop)
Mpz = kron(sz, idop)
else:
print('what model???')
key += args.model \
+ '_D' + str(args.D) \
+ '_chi' + str(args.chi)
if (args.float32):
key += '_float32'
cmd = ['mkdir', '-p', key]
subprocess.check_call(cmd)
if args.model == 'TFIM':
sx = torch.tensor([[0, 1], [1, 0]], dtype=dtype, device=device)
sy = torch.tensor([[0, -1], [1, 0]], dtype=dtype, device=device)
sz = torch.tensor([[1, 0], [0, -1]], dtype=dtype, device=device)
id2 = torch.tensor([[1, 0], [0, 1]], dtype=dtype, device=device)
H = - 2*args.Jz*kron(sz,sz)-args.hx*(kron(sx,id2)+kron(id2,sx))/2
Mpx = (kron(id2,sx) + kron(sx,id2))/2
Mpy = (kron(id2,sy) + kron(sy,id2))/2
Mpz = (kron(id2,sz) + kron(sz,id2))/2
elif args.model == 'Heisenberg':
#Hamiltonian operators on a bond
sx = torch.tensor([[0, 1], [1, 0]], dtype=dtype, device=device)*0.5
sy = torch.tensor([[0, -1], [1, 0]], dtype=dtype, device=device)*0.5
sp = torch.tensor([[0, 1], [0, 0]], dtype=dtype, device=device)
sm = torch.tensor([[0, 0], [1, 0]], dtype=dtype, device=device)
sz = torch.tensor([[1, 0], [0, -1]], dtype=dtype, device=device)*0.5
id2 = torch.tensor([[1, 0], [0, 1]], dtype=dtype, device=device)
# now assuming Jz>0, Jxy > 0
H = 2*args.Jz*kron(sz,4*sx@sz@sx)-args.Jxy*(kron(sm, 4*sx@sp@sx)+kron(sp,4*sx@sm@sx))