# Approximations of Interface Topological Invariants SIAM Journal on Mathematical Analysis. Published: 2024-08-05. 1 citation. ## Authors - Solomon Quinn (University of Minnesota): h-index 3; 27 citations - Guillaume Bal (University of Illinois Chicago): h-index 35; 4,218 citations ## Topics - Markov Chains and Monte Carlo Methods - Theoretical and Computational Physics - Advanced Mathematical Modeling in Engineering ## Funding - National Science Foundation --- # Approximations of interface topological invariants ## Abstract 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 discretizatio