What’s new in Kwant 1.3#

This article explains the user-visible changes in Kwant 1.3.0, released on 19 May 2017. See also the full list of changes up to the most recent bugfix release of the 1.3 series.

Using high-symmetry builders as models#

Builders now have a fill method that fills a builder instance with copies of a template builder. This can be used to “cut out” shapes from high-symmetry models, or to increase the symmetry period of a lead.

Thus Kwant gains the new concept of a “model”. Models may be created manually, or with the new function kwant.continuum.discretize (see next paragraph). There is also support for finalizing models and e.g. calculating their band structure (see Finalizing builders with multiple translational symmetries).

Tools for continuum Hamiltonians#

The new sub-package continuum is a collection of tools for working with continuum models and for discretizing them into tight-binding models. It aims at providing a handy interface to convert symbolic Hamiltonians into a builder with N-D translational symmetry that can be use to calculate tight-binding band structures or construct systems with different/lower symmetry. For example in just a few lines we can construct a two-band model that exhibits a quantum anomalous spin Hall phase:

# Comprehensive example: quantum anomalous Hall effect
# ====================================================
#
# Physics background
# ------------------
# + Quantum anomalous Hall effect
#
# Features highlighted
# --------------------
# + Use of `kwant.continuum` to discretize a continuum Hamiltonian
# + Use of `kwant.operator` to compute local current
# + Use of `kwant.plotter.current` to plot local current

import math
import matplotlib.pyplot
import kwant
import kwant.continuum

import matplotlib
import matplotlib.pyplot
from matplotlib_inline.backend_inline import set_matplotlib_formats

matplotlib.rcParams['figure.figsize'] = matplotlib.pyplot.figaspect(1) * 2
set_matplotlib_formats('svg')

def make_model(a):
    ham = ("alpha * (k_x * sigma_x - k_y * sigma_y)"
           "+ (m + beta * kk) * sigma_z"
           "+ (gamma * kk + U) * sigma_0")
    subs = {"kk": "k_x**2 + k_y**2"}
    return kwant.continuum.discretize(ham, locals=subs, grid=a)

From: plot_qahe.py

See the tutorial: Discretizing continuous Hamiltonians

See the reference documentation: kwant.continuum – Tools for continuum systems

Calculating charges and currents using the operator module#

Often one may wish to calculate quantities that are defined over sites of the system (such as charge density, spin density along some axis etc), or over hoppings of the system (such as current or spin current). With the introduction of the operator module it has now become much easier to calculate such quantities. To obtain the regular density and current everywhere in a system due to a wavefunction psi, one only needs to do the following:

syst = make_system().finalized()
psi = kwant.wave_function(syst)(0)[0]

# create the operators
Q = kwant.operator.Density(syst)
J = kwant.operator.Current(syst)

# evaluate the expectation value with the wavefunction
q = Q(psi)
j = J(psi)

See the tutorial: Computing local quantities: densities and currents

Plotting of currents#

Quantities defined on system hoppings (e.g. currents calculated using Current) can be directly plotted as a streamplot over the system using kwant.plotter.current. This is similar to how kwant.plotter.map can be used to plot quantities defined on sites. The example below shows edge states of a quantum anomalous Hall phase of the two-band model shown in the above section:

def make_system(model, L):
    def lead_shape(site):
        x, y = site.pos / L
        return abs(y) < 0.5

    # QPC shape: a rectangle with 2 gaussians
    # etched out of the top and bottom edge.
    def central_shape(site):
        x, y = site.pos / L
        return abs(x) < 3/5 and abs(y) < 0.5 - 0.4 * math.exp(-40 * x**2)

    lead = kwant.Builder(kwant.TranslationalSymmetry(
        model.lattice.vec((-1, 0))))
    lead.fill(model, lead_shape, (0, 0))

    syst = kwant.Builder()
    syst.fill(model, central_shape, (0, 0))
    syst.attach_lead(lead)
    syst.attach_lead(lead.reversed())

    return syst.finalized()

# Set up our model and system, and define the model parameters.
params = dict(alpha=0.365, beta=0.686, gamma=0.512, m=-0.01, U=0)
model = make_model(1)
syst = make_system(model, 70)

# Calculate the scattering states at energy 'm' coming from the left
# lead, and the associated particle current.
psi = kwant.wave_function(syst, energy=params['m'], params=params)(0)

J = kwant.operator.Current(syst).bind(params=params)
current = sum(J(p) for p in psi)
kwant.plotter.current(syst, current);

From: plot_qahe.py

Scattering states with discrete symmetries and conservation laws#

Given a lead Hamiltonian that has a conservation law, it is now possible to construct lead modes that have definite values of the conservation law. This is done by declaring projectors that block diagonalize the Hamiltonian before the modes are computed. For a Hamiltonian that has one or more of the three fundamental discrete symmetries (time-reversal symmetry, particle-hole symmetry and chiral symmetry), it is now possible to declare the symmetries in Kwant. The symmetries are then used to construct scattering states that are properly related by symmetry. The discrete symmetries may be combined with conservation laws, such that if different blocks of the Hamiltonian are related by a discrete symmetry, the lead modes are computed to reflect this.

See the updated tutorial: Superconductors: orbital degrees of freedom, conservation laws and symmetries

Named parameters for value functions#

In Kwant < 1.3 whenever Hamiltonian values were provided as functions, they all had to take the same extra parameters (after the site(s)) regardless of whether or not they actually used them at all. For example, if we had some onsite potential and a magnetic field that we model using the Peierls substitution, we would have to define our value functions like so:

# formally depends on 'B', but 'B' is never used
def onsite(site, V, B):
    return V

# formally depends on 'V', but 'V' is never used
def hopping(site_a, site_b, V, B):
    return (site_b.pos[1] - site_a.pos[1]) * B

This was because previously extra arguments were provided to the system by passing them as a sequence via the args parameter to various Kwant functions (e.g. kwant.smatrix or hamiltonian_submatrix).

In Kwant 1.3 it is now possible for value functions to depend on different parameters, e.g.:

def onsite(site, V):
    return V

def hopping(site_a, site_b, B):
    return (site_b.pos[1] - site_a.pos[1]) * B

If you make use of this feature then you must in addition pass your arguments via the params parameter. The value provided to params must be a dict that maps parameter names to values, e.g.:

kwant.smatrix(syst, params=dict(B=0.1, V=2))

as opposed to the old way:

kwant.smatrix(syst, args=(2, 0.1))

Passing a dictionary of parameters via params is now the recommended way to provide parameters to the system.

Reference implementation of the kernel polynomial method#

The kernel polynomial method is now implemented within Kwant to obtain the density of states or, more generally, the spectral density of a given operator acting on a system or Hamiltonian.

See the tutorial: Calculating spectral density with the kernel polynomial method

See the reference documentation: kwant.kpm – Kernel Polynomial Method

Finalizing builders with multiple translational symmetries#

While it remains impossible to finalize a builder with more than a single direction of translational symmetry, the wraparound module has been added as a temporary work-around until the above limitation gets lifted.

The function wraparound transforms all (or all but one) translational symmetries of a given builder into named momentum parameters k_x, k_y, etc. This makes it easy to compute transport through systems with periodic boundary conditions or across infinite planes.

Plotting the 2-d band structure of graphene is now as straightforward as:

from matplotlib import pyplot
import kwant

lat = kwant.lattice.honeycomb()
sym = kwant.TranslationalSymmetry(lat.vec((1, 0)), lat.vec((0, 1)))

bulk = kwant.Builder(sym)
bulk[ [lat.a(0, 0), lat.b(0, 0)] ] = 0
bulk[lat.neighbors()] = 1
wrapped = kwant.wraparound.wraparound(bulk).finalized()
kwant.wraparound.plot_2d_bands(wrapped)

Consistent ordering of sites in finalized builders#

In Python 3 the internal ordering of dictionaries is not deterministic. This meant that running a Kwant script twice would produce systems with different ordering of sites, which leads to non-reproducible calculations. Now, sites in finalized builders are always ordered first by their site family, then by their tag.

Coincidentally, this means that you can plot a wavefunction in a simple 1D system by just saying:

lattice_1D = chain()
syst = make_system(lattice_1D)
h = syst.hamiltonian_submatrix()
pyplot.plot(np.eigs(h)[1][0])

attach_lead() can now handle leads with greater than nearest-neighbor hoppings#

When attaching a lead with greater than nearest-neighbor hoppings, the symmetry period of the finalized lead is suitably extended and the unit cell size is increased.

Pickling support#

It is now possible to pickle and unpickle Builder and System instances.

Improved build configuration#

The name of the build configuration file, build.conf by default, is now configurable with the --configfile=PATH option to setup.py. (This makes build configuration usable with the pip tool.) The build configuration as specified in this file is now more general, allowing to modify any build parameter for any of the compiled extensions contained in Kwant. See the Installation instructions for details.

Builder.neighbors() respects symmetries#

Given a site, the method neighbors of Builder returns an iterator over sites that are connected by a hopping to the provided site. This is in contrast to previous versions of Kwant, where the neighbors were yielded not of the provided site, but of it’s image in the fundamental domain.

This change is documented here for completeness. We expect that the vast majority of users of Kwant will not be affected by it.

API change that affects low-level systems#

The hamiltonian method of low-level systems must now accept a params keyword parameter.

What’s new in Kwant 1.3

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