The self-consistent quantum-electrostatic (also known as
Poisson-Schrödinger) problem is notoriously difficult in situations
where the density of states varies rapidly with energy. At low
temperatures, these fluctuations make the problem highly non-linear
which renders iterative schemes deeply unstable. We present a stable
algorithm that provides a solution to this problem with controlled
accuracy. The technique is intrinsically convergent even in highly
non-linear regimes. We illustrate our approach with both a calculation
of the compressible and incompressible stripes in the integer quantum
Hall regime as well as a calculation of the differential conductance of
a quantum point contact geometry. Our technique provides a viable route
for the predictive modeling of the transport properties of quantum
nanoelectronics devices.
Lattice realization of a bosonic integer quantum Hall state–trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model