netket.symmetry

(Work in progress)

Note

To construct a symmetrized ansatz of the form \(\log(O\lvert\psi\rangle)\) where \(O\) is a symmetry projector, see Apply Operator in netket.vqs.apply_operator().

Module with classes and utilities needed to operate on symmetry groups and their representations.

The theory needed to understand those tools is discussed in Representation theory in NetKet and an example notebook is in Symmetries, Representations and Projectors for arbitrary NQS

Common Symmetry Representations

spin_flip_representation	Construct the \(\mathbb{Z}_2\) representation generated by spin flip.
canonical_representation	Construct the representation of a permutation group on a many-body Hilbert space where each permutation is mapped to the permutation operator that permutes the local operators.

Representation Classes

Representation	A representation of a group.
LabeledRepresentation	A Representation with automatic irrep labeling.
TranslationRepresentation	A Representation for the translation group of a Lattice, with Bloch-momentum indexing.

Symmetry Group Manipulation

group.FiniteGroup	Collection of Elements expected to satisfy group axioms.
group.Permutation
group.PermutationGroup	Collection of permutation operations acting on sequences of length degree.
group.cyclic_group	Returns the cyclic PermutationGroup \(\mathbb{Z}_n\) acting on \(n\) elements by cyclic shifts.
group.PGSymmetry	An abstract group element object to geometrically describe point group symmetries.
group.PointGroup	Collection of point group symmetries acting on n-dimensional vectors.

Common Groups

group.axial	3D axial symmetry groups and transformations.
group.planar	2D planar symmetry groups and transformations.
group.cubic	Cubic and related 3D symmetry groups.
group.icosa	Icosahedral symmetry groups.

Internal Objects

These classes are returned by methods such as coset_filter() but are not part of the public netket.symmetry namespace. They are documented here for reference.

labeled_representation_coset_filter.LabeledRepresentationCosetFilter	Coset refinement operator for G/H where G and H are finite groups.
translation_coset_filter.TranslationCosetFilter	Fourier filter for the coset G/H of two translation representations.