def test_flip_state_fock_infinite():
hi = Fock(N=2)
rng = nk.jax.PRNGSeq(1)
N_batches = 20
states = hi.random_state(rng.next(), N_batches, dtype=jnp.int64)
ids = jnp.asarray(
jnp.floor(hi.size *
jax.random.uniform(rng.next(), shape=(N_batches, ))),
dtype=int,
)
new_states, old_vals = nk.hilbert.random.flip_state(
hi, rng.next(), states, ids)
assert new_states.shape == states.shape
assert np.all(states >= 0)
states_np = np.asarray(states)
states_new_np = np.array(new_states)
for (row, col) in enumerate(ids):
states_new_np[row, col] = states_np[row, col]
np.testing.assert_allclose(states_np, states_new_np)
def test_inhomogeneous_fock():
hi1 = Fock(n_max=7, N=40)
hi2 = Fock(n_max=2, N=40)
hi = hi1 * hi2
assert hi.size == hi1.size + hi2.size
for i in range(0, 40):
assert hi.size_at_index(i) == 8
assert hi.states_at_index(i) == list(range(8))
for i in range(40, 80):
assert hi.size_at_index(i) == 3
assert hi.states_at_index(i) == list(range(3))
def _reorder_kronecker_product(hi, mat, acting_on) -> Tuple[Array, Tuple]:
"""
Reorders the matrix resulting from a kronecker product of several
operators in such a way to sort acting_on.
A conceptual example is the following:
if `mat = Â ⊗ B̂ ⊗ Ĉ` and `acting_on = [[2],[1],[3]`
you will get `result = B̂ ⊗ Â ⊗ Ĉ, [[1], [2], [3]].
However, essentially, A,B,C represent some operators acting on
thei sub-space acting_on[1], [2] and [3] of the hilbert space.
This function also handles any possible set of values in acting_on.
The inner logic uses the Fock.all_states(), number_to_state and
state_to_number to perform the re-ordering.
"""
acting_on_sorted = np.sort(acting_on)
if np.array_equal(acting_on_sorted, acting_on):
return mat, acting_on
# could write custom binary <-> int logic instead of using Fock...
# Since i need to work with bit-strings (where instead of bits i
# have integers, in order to support arbitrary size spaces) this
# is exactly what hilbert.to_number() and viceversa do.
# target ordering binary representation
hi_subspace = Fock(hi.shape[acting_on_sorted[0]] - 1)
for site in acting_on_sorted[1:]:
hi_subspace = hi_subspace * Fock(hi.shape[site] - 1)
hi_unsorted_subspace = Fock(hi.shape[acting_on[0]] - 1)
for site in acting_on[1:]:
hi_unsorted_subspace = hi_unsorted_subspace * Fock(hi.shape[site] - 1)
# find how to map target ordering back to unordered
acting_on_unsorted_ids = np.zeros(len(acting_on), dtype=np.intp)
for (i, site) in enumerate(acting_on):
acting_on_unsorted_ids[i] = np.argmax(site == acting_on_sorted)
# now it is valid that
# acting_on_sorted == acting_on[acting_on_unsorted_ids]
# generate n-bit strings in the target ordering
v = hi_subspace.all_states()
# convert them to origin (unordered) ordering
v_unsorted = v[:, acting_on_unsorted_ids]
# convert the unordered bit-strings to numbers in the target space.
n_unsorted = hi_unsorted_subspace.states_to_numbers(v_unsorted)
# reorder the matrix
mat_sorted = mat[n_unsorted, :][:, n_unsorted]
return mat_sorted, tuple(acting_on_sorted)
def _reorder_matrix(hi, mat, acting_on):
acting_on_sorted = np.sort(acting_on)
if np.all(acting_on_sorted == acting_on):
return mat, acting_on
acting_on_sorted_ids = np.argsort(acting_on)
# could write custom binary <-> int logic instead of using Fock...
# Since i need to work with bit-strings (where instead of bits i
# have integers, in order to support arbitrary size spaces) this
# is exactly what hilbert.to_number() and viceversa do.
# target ordering binary representation
hi_subspace = Fock(hi.shape[acting_on_sorted[0]] - 1)
for site in acting_on_sorted[1:]:
hi_subspace = Fock(hi.shape[site] - 1) * hi_subspace
# find how to map target ordering back to unordered
acting_on_unsorted_ids = np.zeros(len(acting_on), dtype=np.intp)
for (i, site) in enumerate(acting_on):
acting_on_unsorted_ids[i] = np.argmax(site == acting_on_sorted)
# now it is valid that
# acting_on_sorted == acting_on[acting_on_unsorted_ids]
# generate n-bit strings in the target ordering
v = hi_subspace.all_states()
# convert them to origin (unordered) ordering
v_unsorted = v[:, acting_on_unsorted_ids]
# convert the unordered bit-strings to numbers in the target space.
n_unsorted = hi_subspace.states_to_numbers(v_unsorted)
# reorder the matrix
mat_sorted = mat[n_unsorted, :][:, n_unsorted]
return mat_sorted, acting_on_sorted
def test_random_states_fock_infinite():
hi = Fock(N=2)
rstate = hi.random_state(jax.random.PRNGKey(14), 20)
assert np.all(rstate >= 0)
assert rstate.shape == (20, 2)
# Spin 1/2 with total Sz
hilberts["Spin[0.5, N=20, total_sz=1"] = Spin(s=0.5, total_sz=1.0, N=20)
hilberts["Spin[0.5, N=5, total_sz=-1.5"] = Spin(s=0.5, total_sz=-1.5, N=5)
# Spin 1/2 with total Sz
hilberts["Spin 1 with total Sz, even sites"] = Spin(s=1.0, total_sz=5.0, N=6)
# Spin 1/2 with total Sz
hilberts["Spin 1 with total Sz, odd sites"] = Spin(s=1.0, total_sz=2.0, N=7)
# Spin 3
hilberts["Spin 3"] = Spin(s=3, N=25)
# Boson
hilberts["Fock"] = Fock(n_max=5, N=41)
# Boson with total number
hilberts["Fock with total number"] = Fock(n_max=3, n_particles=110, N=120)
# Composite Fock
hilberts["Fock * Fock (indexable)"] = Fock(n_max=5, N=4) * Fock(n_max=7, N=4)
hilberts["Fock * Fock (non-indexable)"] = Fock(n_max=4, N=40) * Fock(n_max=7,
N=40)
# Qubit
hilberts["Qubit"] = nk.hilbert.Qubit(100)
# Custom Hilbert
hilberts["Custom Hilbert"] = CustomHilbert(local_states=[-1232, 132, 0], N=70)
# Spin 1/2 with total Sz hilberts["Spin[0.5, N=20, total_sz=1"] = Spin(s=0.5, total_sz=1.0, N=20) hilberts["Spin[0.5, N=5, total_sz=-1.5"] = Spin(s=0.5, total_sz=-1.5, N=5) # Spin 1/2 with total Sz hilberts["Spin 1 with total Sz, even sites"] = Spin(s=1.0, total_sz=5.0, N=6) # Spin 1/2 with total Sz hilberts["Spin 1 with total Sz, odd sites"] = Spin(s=1.0, total_sz=2.0, N=7) # Spin 3 hilberts["Spin 3"] = Spin(s=3, N=25) # Boson hilberts["Fock"] = Fock(n_max=5, N=41) # Boson with total number hilberts["Fock with total number"] = Fock(n_max=3, n_particles=110, N=120) # Qubit hilberts["Qubit"] = nk.hilbert.Qubit(100) # Custom Hilbert hilberts["Custom Hilbert"] = CustomHilbert(local_states=[-1232, 132, 0], N=70) # Heisenberg 1d hilberts["Heisenberg 1d"] = Spin(s=0.5, total_sz=0.0, N=20) # Bose Hubbard hilberts["Bose Hubbard"] = Fock(n_max=4, n_particles=20, N=20)