A topological pump on an $N\text{−}\mathrm{leg}$ spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of $2N\text{−}\mathrm{site}$ staircase clusters. We define a pump path in parameter space that connects two distinct symmetry-protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump, the bulk Chern number is given by the number of critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated in association with deformation of the pump path. We find that there are $N$ critical points enclosed by the pump path for the $N\text{−}\mathrm{leg}$ ladder. The ground-state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states at the diagonal boundary and numerically demonstrate the bulk-edge correspondence for $N=2,3$ cases.

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• Symmetry protected topological states
• Topological materials
• Density matrix renormalization group
• Exact diagonalization
• Spin lattice models