Topological properties of lattice solitons in the two-dimensional Harper-Hofstadter model

Since the discovery of the integer quantum Hall effect, topological 2D lattice models have attracted significant interest in many-body physics. Recent experiments investigating solitons in waveguides with nonlinear Kerr media [1] have observed interaction-induced transitions between phases of integer and fractional quantized topological transport in 1D lattice models.

In one-dimensional systems a quantum mechanical description of lattice solitons is typically done by exact diagonalization or tensor network approaches. These approaches are however strongly limited by system size or not suitable in higher dimensions. Mapping the interacting many-body model of quantum solitons to an effective description of compact objects in a reduced Hilbert-space was successful in reproducing topological properties in 1D models [2]. Motivated by this we here present an effective description of quantum solitons in an interacting two dimensional Harper-Hofstadter model. With this we show the emergence of effective Peierls phases for the composite object which vary with the particle number and in particular cases can destroy the system’s topological properties altogether.

[1]: Jürgensen et. al., Nature 596, 63-67 (2021)

[2]: Bohm et. al., arXiv:2506.00090 (2025)