[FR] Euclidian distance between nodes in nk.graph.lattice

[oliviersimard]

Hi,

Netket provides a method comprised in the class "netket.graph.Lattice" named "distances" which prints out the Manhattan distance between all nodes of the lattice graph (https://netket.readthedocs.io/en/latest/api/_generated/graph/netket.graph.Lattice.html#netket.graph.Lattice.distances). It would be nice to have a similar method that would provide the Euclidian distance between the nodes, taking into account the periodic boundary conditions, having the form:

@partial(jax.vmap, in_axes=(0,None), out_axes=0)
@partial(jax.vmap, in_axes=(None,0), out_axes=0)
def euclidian_distances(p, q):
    assert p.shape == (2,)
    assert q.shape == (2,)

    return jnp.linalg.norm(p-q)

Note that the function above does not consider the periodic boundary conditions.

Thanks :)

[gcarleo]

Hi, on a graph it is generally not well specified what the euclidean distance is, so that's why we have not implemented it in the general case.
To get the euclidean distance you would need to work with specific geometries that are embedded in an euclidean space, for example netket.graph.Lattice. In this case I agree it might be nice to have a distance function (I thought we already had it though? @gpescia maybe knows)

[gpescia]

There is a distance function, taking into account periodic boundary conditions, for a given geometry here: #1583

@oliviersimard I'd say you can use that code for the lattice as well. You just have to define the basis vectors for your lattice (e.g. in a 2D square lattice of size 4x5 the basis vectors would be e1=(4,0) and e2=(0,5)) and express your state vectors in terms of these lattice vectors (e.g. a spin at site (3,1) would have position (3/4 e1 + 1/5 e2)). This conversion should already be provided using from_standard_to_basis in the same PR.

[PhilipVinc]

This issue is just a reminder that we should implement a distance function for the lattice class.