kwant.system.Symmetry[source]¶Bases: object
Abstract base class for spatial symmetries.
Many physical systems possess a discrete spatial symmetry, which results in special properties of these systems. This class is the standard way to describe discrete spatial symmetries in Kwant. An instance of this class can be passed to a Builder instance at its creation. The most important kind of symmetry is translational symmetry, used to define scattering leads.
Each symmetry has a fundamental domain – a set of sites and hoppings,
generating all the possible sites and hoppings upon action of symmetry
group elements. A class derived from Symmetry has to implement mapping
of any site or hopping into the fundamental domain, applying a symmetry
group element to a site or a hopping, and a method which to determine the
group element bringing some site from the fundamental domain to the
requested one. Additionally, it has to have a property num_directions
returning the number of independent symmetry group generators (number of
elementary periods for translational symmetry).
A ValueError must be raised by the symmetry class whenever a symmetry
is used together with sites whose site family is not compatible with it. A
typical example of this is when the vector defining a translational
symmetry is not a lattice vector.
The type of the domain objects as handled by the methods of this class is not specified. The only requirement is that it must support the unary minus operation. The reference implementation of to_fd() is hence self.act(-self.which(a), a, b).
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).
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.
subgroup(*generators)[source]¶Return the subgroup generated by a sequence of group elements.
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