1.5.rst

What's new in Kwant 1.5

This article explains the user-visible changes in Kwant 1.5.0.

Value functions may now be vectorized

It is now possible to define value functions that act on whole arrays of sites at a time.

def onsite(sites):
    r = sites.positions()
    return np.exp(-np.linalg.norm(r, axis=1)**2)

def hopping(to_sites, from_sites):
    dr = to_sites.positions() - from_sites.positions()
    return 1 / np.linalg.norm(dr, axis=1)**2


lat = kwant.lattice.square(norbs=1)
syst = kwant.Builder(vectorize=True)
syst[(lat(i, j) for i in range(4) for j in range(10)] = onsite
syst[lat.neighbors()] = hopping
syst = syst.finalized()

syst.hamiltonian_submatrix()

Notice that when creating the Builder we provide the vectorize=True flag, and that the value functions now take ~kwant.system.SiteArray objects (which have a positions method, rather than a pos property as for ~kwant.system.Site). We can now operate on the array of site positions using numpy. Using vectorized value functions in this way can produce an order of magnitude speedup when evaluating system Hamiltonians (though this speedup may be masked by other parts of your computation e.g. calculating the scattering matrix).

Deprecation of leaving 'norbs' unset for site families

When constructing site families (e.g. lattices) it is now deprecated to leave the 'norbs' parameter unset. This will now raise a KwantDeprecationWarning and will be disallowed in a future version of Kwant. For example, when constructing a square lattice with 1 orbital per site, use:

kwant.lattice.square(norbs=1)

rather than:

kwant.lattice.square()

Automatic addition of Peierls phase terms to Builders

Kwant 1.4 introduced kwant.physics.magnetic_gauge for computing Peierls phases for arbitrary geometries and for systems with leads. Using this functionality requires that the system value functions are equipped to take the required Peierls phase parameters, which is not possible when you are not in direct control of the value functions (e.g. discretized systems). In Kwant 1.5 we have added the missing piece of functionality, kwant.builder.add_peierls_phase, which properly adds the Peierls phase parameters to a Builder's value functions:

syst = make_system()
lead = make_lead()
syst.attach_lead(lead)
syst.attach_lead(lead.reversed())

fsyst, phase = kwant.builder.add_peierls_phase(syst)

def B_syst(pos):
    return np.exp(-np.sum(pos * pos))

kwant.smatrix(fsyst, parameters=dict(t=-1, **phase(B_syst, 0, 0)))

Improved tutorial building

Improving or adding to Kwant's tutorial is now much simpler. Now the text and code for each tutorial is kept in the same file, making it easy to see where changes need to be made, and images generated by the code are inserted directly into the document thanks to the magic of jupyter-sphinx. It has never been easier to get started contributing to Kwant by helping us improve our documentation.

Discretization onto a Landau level basis

The Hamiltonian for a system infinite in at least two dimensions and with a constant applied magnetic field may be expressed in a basis of Landau levels. The momenta in the plane perpendicular to the magnetic field direction are written in terms of the Landau level ladder operators:

k_x = \sqrt{\frac{B}{2}} (a + a^\dagger) \quad\quad
k_y = i \sqrt{\frac{B}{2}} (a - a^\dagger)

The Hamiltonian is then expressed in terms of these ladder operators, which allows for a straight-forward discretization in the basis of Landau levels, provided that the basis is truncated after $N$ levels. kwant.continuum.discretize_landau makes this procedure simple:

syst = kwant.continuum.discretize_landau("k_x**2 + k_y**2", N)
syst.finalized().hamiltonian_submatrix(params=dict(B=0.5))

~kwant.continuum.discretize_landau produces a regular Kwant Builder that can be inspected or finalized as usual. 3D Hamiltonians for systems that extend into the direction perpendicular to the magnetic field are also possible:

template = kwant.continuum.discretize_landau("k_x**2 + k_y**2 + k_z**2 + V(z)", N)

This will produce a Builder with a single translational symmetry, which can be directly finalized, or can be used as a template for e.g. a heterostructure stack in the direction of the magnetic field:

def stack(site):
    z, = site.pos
    return 0 <= z < 10

template = kwant.continuum.discretize_landau("k_x**2 + k_y**2 + k_z**2 + V(z)", N)
syst = kwant.Builder()
syst.fill(template, stack, (0,))