def test_simple_operators():
L = 4
g = nk.graph.Hypercube(L, 1)
hi = nk.hilbert.Spin(g, 0.5)
sx = [[0, 1], [1, 0]]
sy = [[0, -1.0j], [1.0j, 0]]
sz = [[1, 0], [0, -1]]
sm = [[0, 0], [1, 0]]
sp = [[0, 1], [0, 0]]
print("Testing Sigma_x/y/z...")
for i in range(L):
sx_hat = nk.operator.LocalOperator(hi, sx, [i])
sy_hat = nk.operator.LocalOperator(hi, sy, [i])
sz_hat = nk.operator.LocalOperator(hi, sz, [i])
assert (sigmax(hi, i).to_dense() == sx_hat.to_dense()).all()
assert (sigmay(hi, i).to_dense() == sy_hat.to_dense()).all()
assert (sigmaz(hi, i).to_dense() == sz_hat.to_dense()).all()
print("Testing Sigma_+/-...")
for i in range(L):
sm_hat = nk.operator.LocalOperator(hi, sm, [i])
sp_hat = nk.operator.LocalOperator(hi, sp, [i])
assert (sigmam(hi, i).to_dense() == sm_hat.to_dense()).all()
assert (sigmap(hi, i).to_dense() == sp_hat.to_dense()).all()
print("Testing Sigma_+/- composition...")
hi = nk.hilbert.Spin(g, 0.5)
for i in range(L):
sx = sigmax(hi, i)
sy = sigmay(hi, i)
sigmam_hat = 0.5 * (sx + (-1j) * sy)
sigmap_hat = 0.5 * (sx + (1j) * sy)
assert (sigmam(hi, i).to_dense() == sigmam_hat.to_dense()).all()
assert (sigmap(hi, i).to_dense() == sigmap_hat.to_dense()).all()
print("Testing create/destroy composition...")
hi = nk.hilbert.Boson(g, 3)
for i in range(L):
a = bdestroy(hi, i)
ad = bcreate(hi, i)
n = bnumber(hi, i)
assert np.allclose(n.to_dense(), (ad * a).to_dense())
assert (ad.to_dense() == a.conjugate().transpose().to_dense()).all()
def test_pauli_algebra(S):
hi = nk.hilbert.Spin(S)**N
for i in range(N):
sx = spin.sigmax(hi, i)
sy = spin.sigmay(hi, i)
sz = spin.sigmaz(hi, i)
sm = spin.sigmam(hi, i)
sp = spin.sigmap(hi, i)
assert_almost_equal(0.5 * (sx - 1j * sy).to_dense(), sm.to_dense())
assert_almost_equal(0.5 * (sx + 1j * sy).to_dense(), sp.to_dense())
assert_almost_equal(0.5 * (sx.to_dense() - 1j * sy.to_dense()),
sm.to_dense())
assert_almost_equal(0.5 * (sx.to_dense() + 1j * sy.to_dense()),
sp.to_dense())
if S == 1 / 2:
Imat = np.eye(hi.n_states)
# check that -i sx sy sz = I
assert_almost_equal((-1j * sx @ sy @ sz).to_dense(), Imat)
assert_almost_equal(
(-1j * sx.to_dense() @ sy.to_dense() @ sz.to_dense()), Imat)
def test_simple_operators():
L = 4
hi = nk.hilbert.Spin(0.5) ** L
sx = [[0, 1], [1, 0]]
sy = [[0, -1.0j], [1.0j, 0]]
sz = [[1, 0], [0, -1]]
sm = [[0, 0], [1, 0]]
sp = [[0, 1], [0, 0]]
print("Testing Sigma_x/y/z...")
for i in range(L):
sx_hat = nk.operator.LocalOperator(hi, sx, [i])
sy_hat = nk.operator.LocalOperator(hi, sy, [i])
sz_hat = nk.operator.LocalOperator(hi, sz, [i])
assert (sigmax(hi, i).to_dense() == sx_hat.to_dense()).all()
assert (sigmay(hi, i).to_dense() == sy_hat.to_dense()).all()
assert (sigmaz(hi, i).to_dense() == sz_hat.to_dense()).all()
print("Testing Sigma_+/-...")
for i in range(L):
sm_hat = nk.operator.LocalOperator(hi, sm, [i])
sp_hat = nk.operator.LocalOperator(hi, sp, [i])
assert (sigmam(hi, i).to_dense() == sm_hat.to_dense()).all()
assert (sigmap(hi, i).to_dense() == sp_hat.to_dense()).all()
print("Testing Sigma_+/- composition...")
hi = nk.hilbert.Spin(0.5, N=L)
for i in range(L):
sx = sigmax(hi, i)
sy = sigmay(hi, i)
sigmam_hat = 0.5 * (sx + (-1j) * sy)
sigmap_hat = 0.5 * (sx + (1j) * sy)
assert (sigmam(hi, i).to_dense() == sigmam_hat.to_dense()).all()
assert (sigmap(hi, i).to_dense() == sigmap_hat.to_dense()).all()
print("Testing create/destroy composition...")
hi = nk.hilbert.Fock(3, N=L)
for i in range(L):
print("i=", i)
a = bdestroy(hi, i)
ad = bcreate(hi, i)
n = bnumber(hi, i)
assert np.allclose(n.to_dense(), (ad @ a).to_dense())
assert (ad.to_dense() == a.conjugate().transpose().to_dense()).all()
print("Testing mixed spaces...")
L = 3
his = nk.hilbert.Spin(0.5, N=L)
hib = nk.hilbert.Fock(3, N=L - 1)
hi = his * hib
for i in range(hi.size):
print("i=", i)
sx = sigmax(hi, i)
assert sx.operators[0].shape == (hi.shape[i], hi.shape[i])
assert np.allclose(n.to_dense(), (ad @ a).to_dense())
assert (ad.to_dense() == a.conjugate().transpose().to_dense()).all()
for i in range(3):
print("i=", i)
a = bdestroy(hi, i)
ad = bcreate(hi, i)
n = bnumber(hi, i)
for j in range(3, 5):
print("j=", i)
a = bdestroy(hi, j)
ad = bcreate(hi, j)
n = bnumber(hi, j)
assert np.allclose(n.to_dense(), (ad @ a).to_dense())
assert (ad.to_dense() == a.conjugate().transpose().to_dense()).all()
from netket.operator import spin
np.set_printoptions(linewidth=180)
# 1D Lattice
L = 4
# Hilbert space of spins on the graph
hi = nk.hilbert.Spin(s=0.5) ** L
ha = nk.operator.LocalOperator(hi, dtype=complex)
j_ops = []
for i in range(L):
ha += spin.sigmax(hi, i)
ha += spin.sigmay(hi, i)
ha += spin.sigmaz(hi, i) @ spin.sigmaz(hi, (i + 1) % L)
j_ops.append(spin.sigmam(hi, i))
j_ops.append(1j * spin.sigmam(hi, i))
# Create the lindbladian with
lind = nk.operator.LocalLiouvillian(ha, j_ops)
def test_lindblad_form():
## Construct the lindbladian by hand:
idmat = sparse.eye(2**L)
# Build the non hermitian matrix