quantax.symmetry.Translation

class quantax.symmetry.Translation

Bases: Symmetry

Translation symmetry.

__init__(vectors: Sequence, sector: int = 0)

Translation symmetry.

Parameters:

• vectors – The translation vectors, in the unit of lattice basis vectors.

• sector – The symmetry sector.

property vectors: ndarray

The translation vectors.

get_sublattice_coord() → ndarray

Get the coordinate of lattice sites in the sublattice.

property Z2_inversion: int

The Z2 inversion symmetry. It represents the spin flip in spin-1/2 systems, and the particle-hole symmetry in fermionic systems. The meaning of each number is

• 1: Eigenvalue 1 after Z2 inversion

• 0: No Z2 inversion symmetry

• -1: Eigenvalue -1 after Z2 inversion

property basis

The QuSpin basis corresponding to the symmetry.

basis_make() → None

Make the QuSpin basis stored in the symmetry.

property character: Array

Characters \(\chi\) of all group elements.

get_symm_spins(spins: Array) → Array

Get all symmetrized bases \(s'=Ts\) generated by the symmetry permutations.

Parameters:

spins – Input spin or fermion configuration \(s\).

Note

This function is jittable.

property nsymm: int

Number of elements in the symmetry group.

symmetrize(psi: ndarray | Array | LogArray | ScaleArray, spins: Array | None = None) → ndarray | Array | LogArray | ScaleArray

Symmetrize the wavefunction as

\[\psi^{\mathrm{symm}}(s) = \frac{d}{|G|} \sum_g \mathrm{sign}(s, g) \chi_g \psi(T_g s),\]

where \(d\) is the dimension of the group representation, \(|G|\) is the number of elements in the symmetry group, and \(\mathrm{sign}(s, g)\) is the additional sign generated by the symmetry depending on the input Fock state (only for fermionic systems).

Parameters:

• psi – Wavefunctions \(\psi(T_i s)\).

• spins – Input spin or fermion configuration \(s\). This is only necessary in fermionic systems, where additional minus signs \(\mathrm{sign}(s, g)\) can be generated by the symmetry.

Returns:

The symmetrized wave function

Note

This function is jittable.