netket.exact.lanczos_ed

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netket.exact.lanczos_ed#

netket.exact.lanczos_ed(operator, *, k=1, compute_eigenvectors=False, matrix_free=False, scipy_args=None)[source]#

Computes first_n smallest eigenvalues and, optionally, eigenvectors of a Hermitian operator using scipy.sparse.linalg.eigsh().

Parameters:

  • operator (AbstractOperator) – NetKet operator to diagonalize.

  • k (int) – The number of eigenvalues to compute.

  • compute_eigenvectors (bool) – Whether or not to return the eigenvectors of the operator. With ARPACK, not requiring the eigenvectors has almost no performance benefits.

  • matrix_free (bool) – If true, matrix elements are computed on the fly. Otherwise, the operator is first converted to a sparse matrix.

  • scipy_args (dict | None) – Additional keyword arguments passed to scipy.sparse.linalg.eigvalsh(). See the Scipy documentation for further information.

Returns:

Either w or the tuple (w, v) depending on whether compute_eigenvectors is True.

  • w: Array containing the lowest first_n eigenvalues.

  • v: Array containing the eigenvectors as columns, such that`v[:, i]` corresponds to w[i].

Example

Test for 1D Ising chain with 8 sites.

>>> import netket as nk
>>> hi = nk.hilbert.Spin(s=1/2)**8
>>> hamiltonian = nk.operator.Ising(hi, h=1.0, graph=nk.graph.Chain(8))
>>> w = nk.exact.lanczos_ed(hamiltonian, k=3)
>>> w
array([-10.25166179, -10.05467898,  -8.69093921])
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