netket.symmetry.spin_flip_representation

netket.symmetry.spin_flip_representation(hilbert)

Construct the \(\mathbb{Z}_2\) representation generated by spin flip.

On a Spin Hilbert space, the non-trivial element acts as \(|m_1, \ldots, m_N\rangle \mapsto |-m_1, \ldots, -m_N\rangle\).

On a SpinOrbitalFermions Hilbert space, the non-trivial element swaps spin subsectors according to \(m_s \mapsto -m_s\), leaving the orbital index unchanged.

Parameters:

hilbert (Spin | SpinOrbitalFermions) – A spin or spinful fermionic Hilbert space.

Return type:

LabeledRepresentation

Returns:

An LabeledRepresentation of \(\mathbb{Z}_2\) with irrep labels ['+1', '-1'] (even/symmetric and odd/antisymmetric sectors respectively).

Raises:

• TypeError – If hilbert is not supported.

• ValueError – If spin flip does not preserve the Hilbert space constraints.