Reproducible on-site disorder in Kwant

On-site disorder should assign one fixed random value to each lattice site for a given sample. Kwant can evaluate an on-site function more than once, so drawing from a mutable random-number generator inside that function can change the Hamiltonian between evaluations. Recreating a generator with the same seed on every call has the opposite problem: every site receives the same first random number.

kwant.digest.uniform provides a convenient alternative. It maps a site identifier and a salt to a reproducible value in the interval $[0,1)$ . For a disorder strength $W$ , define

$V_i = W\left[u(k_i,s)-\frac{1}{2}\right].$

Here $k_i$ identifies a site, and $s$ identifies a disorder realization. The resulting on-site potential is distributed over $[-W/2,W/2)$ .

A complete finite-system example

import kwant
import kwant.digest


def onsite(site, disorder_strength, salt):
    # Include the family so distinct sublattices do not share the same key.
    key = repr((site.family.name, tuple(int(value) for value in site.tag)))
    random_value = kwant.digest.uniform(key, salt=salt)
    return disorder_strength * (random_value - 0.5)


lat = kwant.lattice.square(norbs=1, name="sample")
system = kwant.Builder()
system[(lat(x, y) for x in range(20) for y in range(10))] = onsite
system[lat.neighbors()] = -1.0
finalized = system.finalized()

parameters = {"disorder_strength": 0.5, "salt": "sample-0"}
hamiltonian = finalized.hamiltonian_submatrix(params=parameters, sparse=True)

The hopping sets the energy unit in this example. If the clean model has a nonzero on-site term, add the disorder potential to that term. For a model with several orbitals per site, multiply a scalar disorder potential by the orbital identity matrix before adding it to the clean on-site matrix.

Control the realization explicitly

Keep the same lattice-family names, site tags and salt to reproduce a sample, regardless of the order in which Kwant evaluates the sites.
Change the salt, for example from "sample-0" to "sample-1", to obtain another realization. Record the salt with the physical parameters and the software versions used for a calculation.
Keep the salt fixed while varying disorder_strength to rescale the same spatial pattern. This helps distinguish a change in strength from a change in sample.
If clean leads are required, assign their on-site terms separately instead of applying the disordered function to the leads.

The family name is part of the key. Assign distinct explicit names to different sublattices when constructing a multi-sublattice model. Renaming a family changes the disorder realization even if its coordinates are unchanged.

A complete finite-system example

Control the realization explicitly

References