  This paper concerns the asymmetric transport observed along interfaces
separating two-dimensional bulk topological insulators modeled by (continuous)
differential Hamiltonians and how such asymmetry persists after numerical
discretization. We first demonstrate that a relevant edge current observable is
quantized and robust to perturbations for a large class of elliptic
Hamiltonians. We then establish a bulk edge correspondence stating that the
observable equals an integer-valued bulk difference invariant depending solely
on the bulk phases. We next show how to extend such results to periodized
Hamiltonians amenable to standard numerical discretizations. A form of no-go
theorem implies that the asymmetric transport of periodized Hamiltonians
necessarily vanishes. We introduce a filtered version of the edge current
observable and show that it is approximately stable against perturbations and
converges to its quantized limit as the size of the computational domain
increases. To illustrate the theoretical results, we finally present numerical
simulations that approximate the infinite domain edge current with high
accuracy, and show that it is approximately quantized even in the presence of
perturbations.
