# netket.hilbert.HomogeneousHilbert¶

class netket.hilbert.HomogeneousHilbert(local_states, N=1, constraint_fn=None)

The Abstract base class for homogeneous hilbert spaces.

This class should only be subclassed and should not be instantiated directly.

Inheritance
__init__(local_states, N=1, constraint_fn=None)[source]

Constructs a new HomogeneousHilbert given a list of eigenvalues of the states and a number of sites, or modes, within this hilbert space.

This method should only be called from the subclasses __init__ method.

Parameters
• local_states (list or None) – Eigenvalues of the states. If the allowed states are an infinite number, None should be passed as an argument.

• N (int) – Number of modes in this hilbert space (default 1).

• constraint_fn (Optional[Callable]) – A function specifying constraints on the quantum numbers. Given a batch of quantum numbers it should return a vector of bools specifying whether those states are valid or not.

Attributes
constrained

Returns True if the hilbert space is constrained.

Return type

bool

is_finite

Whether the local hilbert space is finite.

Return type

bool

is_indexable

Whever the space can be indexed with an integer

Return type

bool

local_size

Size of the local degrees of freedom that make the total hilbert space.

Return type

int

local_states

A list of discreet local quantum numbers. If the local states are infinitely many, None is returned.

Return type
n_states

The total dimension of the many-body Hilbert space. Throws an exception iff the space is not indexable.

Return type

int

shape

The size of the hilbert space on every site.

Return type

Tuple[int, …]

size

The total number number of degrees of freedom.

Return type

int

Methods
all_states(out=None)

Returns all valid states of the Hilbert space.

Throws an exception if the space is not indexable.

Parameters

out (Optional[ndarray]) – an optional pre-allocated output array

Return type

ndarray

Returns

A (n_states x size) batch of statess. this corresponds to the pre-allocated array if it was passed.

numbers_to_states(numbers, out=None)

Returns the quantum numbers corresponding to the n-th basis state for input n. n is an array of integer indices such that numbers[k]=Index(states[k]). Throws an exception iff the space is not indexable.

Parameters
• numbers (numpy.array) – Batch of input numbers to be converted into arrays of quantum numbers.

• out (Optional[ndarray]) – Optional Array of quantum numbers corresponding to numbers.

Return type

ndarray

ptrace(sites)

Returns the hilbert space without the selected sites.

Not all hilbert spaces support this operation.

Parameters

sites (Union[int, Iterable]) – a site or list of sites to trace away

Return type

AbstractHilbert

Returns

The partially-traced hilbert space. The type of the resulting hilbert space might be different from the starting one.

random_state(key=None, size=None, dtype=<class 'numpy.float32'>)

Generates either a single or a batch of uniformly distributed random states. Runs as random_state(self, key, size=None, dtype=np.float32) by default.

Parameters
• key – rng state from a jax-style functional generator.

• size (Optional[int]) – If provided, returns a batch of configurations of the form (size, N) if size is an integer or (*size, N) if it is a tuple and where $$N$$ is the Hilbert space size. By default, a single random configuration with shape (#,) is returned.

• dtype – DType of the resulting vector.

Return type

ndarray

Returns

A state or batch of states sampled from the uniform distribution on the hilbert space.

Example

>>> import netket, jax
>>> hi = netket.hilbert.Qubit(N=2)
>>> k1, k2 = jax.random.split(jax.random.PRNGKey(1))
>>> print(hi.random_state(key=k1))
[1. 0.]
>>> print(hi.random_state(key=k2, size=2))
[[0. 0.]
[0. 1.]]
size_at_index(i)[source]

Size of the local degrees of freedom for the i-th variable.

Parameters

i (int) – The index of the desired site

Return type

int

Returns

The number of degrees of freedom at that site

states()

Returns an iterator over all valid configurations of the Hilbert space. Throws an exception iff the space is not indexable. Iterating over all states with this method is typically inefficient, and all_states should be prefered.

Return type
states_at_index(i)[source]

A list of discrete local quantum numbers at the site i. If the local states are infinitely many, None is returned.

Parameters

i (int) – The index of the desired site.

Returns

A list of values or None if there are infintely many.

states_to_numbers(states, out=None)

Returns the basis state number corresponding to given quantum states. The states are given in a batch, such that states[k] has shape (hilbert.size). Throws an exception iff the space is not indexable.

Parameters
• states (ndarray) – Batch of states to be converted into the corresponding integers.

• out (Optional[ndarray]) – Array of integers such that out[k]=Index(states[k]). If None, memory is allocated.

Returns

Array of integers corresponding to out.

Return type

numpy.darray