def __init__(
self,
hilbert: AbstractHilbert,
graph: AbstractGraph,
J: float = 1,
sign_rule=None,
):
"""
Constructs an Heisenberg operator given a hilbert space and a graph providing the
connectivity of the lattice.
Args:
hilbert: Hilbert space the operator acts on.
graph: The graph upon which this hamiltonian is defined.
J: The strength of the coupling. Default is 1.
sign_rule: If enabled, Marshal's sign rule will be used. On a bipartite
lattice, this corresponds to a basis change flipping the Sz direction
at every odd site of the lattice. For non-bipartite lattices, the
sign rule cannot be applied. Defaults to True if the lattice is
bipartite, False otherwise.
Examples:
Constructs a ``Heisenberg`` operator for a 1D system.
>>> import netket as nk
>>> g = nk.graph.Hypercube(length=20, n_dim=1, pbc=True)
>>> hi = nk.hilbert.Spin(s=0.5, total_sz=0, graph=g)
>>> op = nk.operator.Heisenberg(hilbert=hi)
>>> print(op.hilbert.size)
20
"""
if sign_rule is None:
sign_rule = graph.is_bipartite()
self._J = J
self._sign_rule = sign_rule
sz_sz = np.array([
[1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, 1],
])
exchange = np.array([
[0, 0, 0, 0],
[0, 0, 2, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
])
if sign_rule:
if not graph.is_bipartite():
raise ValueError(
"sign_rule=True specified for a non-bipartite lattice")
heis_term = sz_sz - exchange
else:
heis_term = sz_sz + exchange
super().__init__(
hilbert,
graph,
bond_ops=[J * heis_term],
)
def __init__(
self,
hilbert: AbstractHilbert,
graph: AbstractGraph,
J: Union[float, Sequence[float]] = 1.0,
sign_rule=None,
*,
acting_on_subspace: Union[List[int], int] = None,
):
"""
Constructs an Heisenberg operator given a hilbert space and a graph providing the
connectivity of the lattice.
Args:
hilbert: Hilbert space the operator acts on.
graph: The graph upon which this hamiltonian is defined.
J: The strength of the coupling. Default is 1.
Can pass a sequence of coupling strengths with coloured graphs:
edges of colour n will have coupling strength J[n]
sign_rule: If True, Marshal's sign rule will be used. On a bipartite
lattice, this corresponds to a basis change flipping the Sz direction
at every odd site of the lattice. For non-bipartite lattices, the
sign rule cannot be applied. Defaults to True if the lattice is
bipartite, False otherwise.
If a sequence of coupling strengths is passed, defaults to False
and a matching sequence of sign_rule must be specified to override it
acting_on_subspace: Specifies the mapping between nodes of the graph and
Hilbert space sites, so that graph node :code:`i ∈ [0, ..., graph.n_nodes - 1]`,
corresponds to :code:`acting_on_subspace[i] ∈ [0, ..., hilbert.n_sites]`.
Must be a list of length `graph.n_nodes`. Passing a single integer :code:`start`
is equivalent to :code:`[start, ..., start + graph.n_nodes - 1]`.
Examples:
Constructs a ``Heisenberg`` operator for a 1D system.
>>> import netket as nk
>>> g = nk.graph.Hypercube(length=20, n_dim=1, pbc=True)
>>> hi = nk.hilbert.Spin(s=0.5, total_sz=0, N=g.n_nodes)
>>> op = nk.operator.Heisenberg(hilbert=hi, graph=g)
>>> print(op)
Heisenberg(J=1.0, sign_rule=True; dim=20)
"""
if isinstance(J, Sequence):
# check that the number of Js matches the number of colours
assert len(J) == max(graph.edge_colors) + 1
if sign_rule is None:
sign_rule = [False] * len(J)
else:
assert len(sign_rule) == len(J)
for i in range(len(J)):
subgraph = Graph(edges=graph.edges(filter_color=i))
if sign_rule[i] and not subgraph.is_bipartite():
raise ValueError(
"sign_rule=True specified for a non-bipartite lattice"
)
else:
if sign_rule is None:
sign_rule = graph.is_bipartite()
elif sign_rule and not graph.is_bipartite():
raise ValueError(
"sign_rule=True specified for a non-bipartite lattice")
self._J = J
self._sign_rule = sign_rule
sz_sz = np.array([
[1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, -1, 0],
[0, 0, 0, 1],
])
exchange = np.array([
[0, 0, 0, 0],
[0, 0, 2, 0],
[0, 2, 0, 0],
[0, 0, 0, 0],
])
if isinstance(J, Sequence):
bond_ops = [
J[i] * (sz_sz - exchange if sign_rule[i] else sz_sz + exchange)
for i in range(len(J))
]
bond_ops_colors = list(range(len(J)))
else:
bond_ops = [
J * (sz_sz - exchange if sign_rule else sz_sz + exchange)
]
bond_ops_colors = []
super().__init__(
hilbert,
graph,
bond_ops=bond_ops,
bond_ops_colors=bond_ops_colors,
acting_on_subspace=acting_on_subspace,
)