kwant.builder.Symmetry¶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.
Methods
act(element, a, b=None)¶Act with a symmetry group element on a site or hopping.
in_fd(site)¶Tell whether site lies within the fundamental domain.
to_fd(a, b=None)¶Map a site or hopping to the fundamental domain.
If b is None, return a site equivalent to a within the fundamental domain. Otherwise, return a hopping equivalent to (a, b) but where the first element belongs to the fundamental domain.
This default implementation works but may be not efficient.
which(site)¶Calculate the domain of the site.
Return the group element whose action on a certain site from the
fundamental domain will result in the given site.
Attributes
num_directions¶Number of elementary periods of the symmetry.