Quantum lattice solitons in a 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. These models can be simulated using ultra-cold atoms in optical lattices [1]. Moreover recent experiments investigating solitons in waveguides with nonlinear Kerr media [2] have observed fractional 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 either 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.

Motivated by this we here present an effective description of quantum solitons in an interacting two-dimensional Harper-Hofstadter model. With this we are able to simulate multiple fractions of soliton transport in the system analog to fractional quantum Hall physics.

[1]: I. Bloch, Rev. Mod. Phys. 80, 885 (2008)

[2]: Jürgensen et. al., Nature 596, 63–67 (2021)