Density-matrix renormalization group (DMRG) simulations of a four-leg ladder, which realizes in (2+1)d the (1+1)d 3-4-5-0 chiral fermion model, show that quantized charge pumping survives at a fully gapped interacting edge. The quantization holds with the same pumped charge per flux quantum across the three boundary phases identified, although the spatial distribution of that charge changes between phases.

The starting point is a well-known topological property: in quantum Hall systems, inserting a flux quantum drives spectral flow through the chiral edge modes, resulting in quantized charge pumping. When the boundary is anomaly-free, symmetric mass generation (SMG) interactions can gap it without breaking the symmetry. Until now, what happened to quantized pumping in that situation was unclear.

The authors add six-fermion interactions at one edge of the 3-4-5-0 model and explore three coupling regimes. For weak and strong couplings, gapless modes appear near the interacting edge, while at intermediate coupling the edge enters a fully gapped SMG phase. Above a critical interaction strength, the model's Z₂ symmetry is also spontaneously broken. In all three phases, the pumped charge per flux quantum turns out to be identical.

The study also examines how a single injected fermion propagates under open boundary conditions. In the SMG phase, an interaction-induced flavor-mixing current develops at the endpoints of the gapped edge, absent in the weak- and strong-coupling limits. This current reveals a charge-redistribution mechanism unique to the SMG phase. The authors further propose an analogy between charge pumping in this model and a topological leptogenesis scenario in the (3+1)d Standard Model: the anomaly-free chiral U(1) symmetries of the 3-4-5-0 model would play a role analogous to baryon-minus-lepton symmetry, and in both cases pumping would be associated with a continuous deformation along a classically defined but quantum-anomalous direction, while a discrete subgroup remains an exact quantum symmetry.