Many-body polarization and topological phases of the Rice-Mele-Hubbard model

The many-body polarization introduced by Resta [1] has been shown to be a powerful tool to distinguish topological phases of one-dimensional lattice models of fermions in the absence or presence of interactions

both in the many-body ground state and for finite temperature states. We here discuss the Rice-Mele model for spinful fermions with local Hubbard interactions at double-half filling, realizing a topological charge pump. It has been shown that for sufficiently strong repulsive interactions the topologically quantized charge transport of 1 + 1 particle per pump cycle either breaks down completely [2,3] or is reduced to a transport of 1/2 + 1/2 particle when appropriately modifying the parameter path. For equal hopping amplitudes and sufficiently strong repulsive interactions the ground state is a doubly degenerate Mott insulator, while the ground state is non-degenerate for alternating hoppings. We show that in the regimes where interactions destroy a quantized particle transport, the many-body polarization of individual spin components still allows to identify topological phases visible e.g. by the presence or absence of edge states. We also discuss the relation between polarization winding and transport in the presence of isolated parameter points with double degeneracy.

[1] R. Resta, Phys. Rev. Lett. 80, 1800 (1998)

[2] M. Nakagawa et al., Phys. Rev. B 98, 115147 (2018)

[3] E. Bertok et al., Phys. Rev. B 106, 045141 (2022)