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Abstract:
We investigate the interacting, one-dimensional Rice-Mele model, a prototypical fermionic model of topological properties. To set the stage, we first compute the single-particle spectral function, the local density, and the boundary charge in the absence of interactions. We find that the fractional part of the boundary charge is fully determined by bulk properties of the lattice model. In a large parameter regime the boundary charge agrees with the one obtained from an effective low-energy theory (arXiv:2004.00463). Second, we investigate the robustness of our results towards two-particle interactions. To resume the series of leading logarithms for small gaps, which dismantle plain perturbation theory in the interaction, we use an essentially analytical renormalization group approach. It is controlled for small interactions and can directly be applied to the microscopic lattice model. We benchmark the results against numerical density matrix renormalization group data. The main interaction effect in the bulk is a power-law renormalization of the gap with an interaction dependent exponent. The important characteristics of the fractional part of the boundary charge are unaltered and can be understood from the renormalized bulk properties. This requires a consistent treatment not only of the low-energy gap renormalization but also of the high-energy band width one. In contrast to low-energy field theories our renormalization group approach also provides the latter. We show that the interaction spoils the relation between the bulk properties and the number of edge states, consistent with the observation that the Rice-Mele model with finite potential modulation does not reveal any zero-energy edge states.
