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netket.hilbert.Particle

netket.hilbert.Particle#

class netket.hilbert.Particle[source]#

Bases: ContinuousHilbert

Hilbert space derived from ContinuousHilbert defining N particles in continuous space with or without periodic boundary conditions.

Inheritance
Inheritance diagram of netket.hilbert.Particle
__init__(N, L=None, pbc=None, *, D=None)[source]#

Constructs new Particles given specifications of the continuous space they are defined in.

Parameters:

  • N (Union[int, tuple[int, ...]]) – Number of particles. If int all have the same spin. If Tuple the entry indicates how many particles there are with a certain spin-projection.

  • L (Optional[tuple[float, ...]]) – Tuple indicating the maximum of the continuous quantum number(s) in the configurations. Each entry in the tuple corresponds to a different physical dimension. If np.inf is used an infinite box is considered and pbc=False is mandatory (because what are PBC if there are no boundaries?). If a finite value is given, a minimum value of zero is assumed for the quantum number(s). A particle in a 3D box of size L would take (L,L,L). A rotor model would take e.g. (2pi,).

  • pbc (Union[bool, tuple[bool, ...], None]) – Tuple or bool indicating whether to use periodic boundary conditions in a given physical dimension. If tuple it must have the same length as domain. If bool the same value is used for all the dimensions defined in domain.

  • D (Optional[int]) – (Optional) Number of dimensions. Can be specified instead of L and pbc in order to construct a Particle in a $D-$ dimensional infinite box. Equivalent to Particle(N, L=(np.inf,) * D, pbc=False).

Attributes
extent#

Spatial extension in each spatial dimension

is_indexable#

Whether the space can be indexed with an integer

n_particles#

The number of particles

n_per_spin#

Gives the number of particles in a specific spin projection.

The length of this tuple indicates the total spin whereas the position in the tuple indicates the spin projection.

Example: (10,5,3) describes 18 particles of total spin 1 where 10 of those have spin-projection -1, 5 have spin-projection 0 and 3 have spin-projection 1.

pbc#

Whether or not to use periodic boundary conditions for each spatial dimension

size#
Methods
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:

Array

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.]]
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