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_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()