kwant.lattice.TranslationalSymmetry(*periods)[source]¶Bases: kwant.system.Symmetry
A translational symmetry defined in real space.
An alias exists for this common name: kwant.TranslationalSymmetry.
Group elements of this symmetry are integer tuples of appropriate length.
p0 (sequences of real numbers) – The symmetry periods in real space.
p1 (sequences of real numbers) – The symmetry periods in real space.
p2 (sequences of real numbers) – The symmetry periods in real space.
.. (sequences of real numbers) – The symmetry periods in real space.
Notes
This symmetry automatically chooses the fundamental domain for each new
SiteFamily it encounters. If this site family does not correspond to a
Bravais lattice, or if it does not have a commensurate period, an error is
produced. A certain flexibility in choice of the fundamental domain can be
achieved by calling manually the add_site_family method and providing it
the other_vectors parameter.
The fundamental domain for hoppings are all hoppings (a, b) with site
a in fundamental domain of sites.
Methods
act(element, a, b=None)[source]¶Act with symmetry group element(s) on site(s) or hopping(s).
element (tuple or sequence of tuples) – Group element(s) with which to act on the provided site(s) or hopping(s)
a (Site or SiteArray) – If Site then element is a single tuple, if SiteArray then
element is a single tuple or a sequence of tuples.
If only a is provided then element acts on the site(s)
of a. If b is also provided then element acts
on the hopping(s) (a, b).
b (Site or SiteArray) – If Site then element is a single tuple, if SiteArray then
element is a single tuple or a sequence of tuples.
If only a is provided then element acts on the site(s)
of a. If b is also provided then element acts
on the hopping(s) (a, b).
add_site_family(fam, other_vectors=None)[source]¶Select a fundamental domain for site family and cache associated data.
fam (SiteFamily) – the site family which has to be processed. Be sure to delete the previously processed site families from site_family_data if you want to modify the cache.
other_vectors (2d array-like of integers) – Bravais lattice vectors used to complement the periods in forming a basis. The fundamental domain consists of all the lattice sites for which the zero coefficients corresponding to the symmetry periods in the basis formed by the symmetry periods and other_vectors. If an insufficient number of other_vectors is provided to form a basis, the missing ones are selected automatically.
KeyError – If fam is already stored in site_family_data.
ValueError – If lattice fam is incompatible with given periods.
has_subgroup(other)[source]¶Test whether self has the subgroup other…
or, in other words, whether other is a subgroup of self. The reason why this is the abstract method (and not is_subgroup) is that in general it’s not possible for a subgroup to know its supergroups.
reversed()[source]¶Return a reversed copy of the symmetry.
The resulting symmetry has all the period vectors opposite to the original and an identical fundamental domain.
subgroup(*generators)[source]¶Return the subgroup generated by a sequence of group elements.
*generators (sequence of int) – Each generator must have length self.num_directions.
to_fd(a, b=None)[source]¶Map a site or hopping to the fundamental domain.
:param : :param b)`` but where the first element belongs to the fundamental domain.: :param Equivalent to self.act(-self.which(a): :param a: :param b).:
Attributes