Topological pump and its plateau transitions of N-leg spin ladder

A topological pump is a quantized charge transport characterized by the Chern number[1] and its applications for spin chains are also considered[2,3]. Generally, the topological pump may exhibit a variety of behaviors depending on the underlying lattice structure and the type of interactions involved. In this study, we consider a topological pump of an N-leg spin ladder[4]. Spatial clusterization whose adiabatic limit is a set of 2N-site clusters is introduced. We firstly investigate the ground state phase diagram by using the quantized Berry phase and find that the ladder has N critical points of symmetry protected topological (SPT) phase transition between two opposite modulation limits. We secondly set a pump path in the parameter space to connect two different SPT phases by introducing a symmetry breaking staggered magnetic field. Plateau transitions by the Chern number are demonstrated associated with deformation of the pump path. We also discuss the behavior of the edge modes of the topological pump.

[1] D. J. Thouless, Phys. Rev. B 27, 6083 (1983).

[2] R. Shindou, J. Phys. Soc. Jpn. 74, 1214 (2005).

[3] Y. Kuno, Y. Hatsugai, Phys. Rev. B 104, 045113 (2021).

[4] K. Yamamoto, Y. Kuno, T. Mizoguchi, K. Sone and Y. Hatusgai, arXiv:2505.01153