Quantum Theory of Topological Phases of Lattice Solitons
Prof. Dr. Michael Fleischhauer (RPTU Kaiserslautern-Landau)

Recent experiments in arrays of optical waveguides have shown (fractionally) quantized topological transport of solitons [1,2]. I will present a fully quantum mechanical description of such topological pumps of bosons with attractive on-site interactions [3]. The transport of bound N-particle composite objects in a 1D lattice upon cyclic adiabatic changes of the Hamiltonian is determined by the elective band-structure of its center-of-mass (COM) motion. If the COM band is energetically separated from all other many-body states in a full cycle the transport is quantized and characterized by a many-body Chern number. Increasing the interaction energy leads to a successive merging of COM bands resulting in topological phase transitions from phases with integer quantized transport through different phases of fractional transport, characterized by a non-trivial Wilson loop, and eventually to a phase without topological transport.

I will discuss an approach to numerically calculate the Chern numbers and Wilson loops for composites that are sufficiently tightly conned. Furthermore, I present a minimal model for which we can explicitly construct an elective single-particle Hamiltonian of the bound object that shows an interaction-induced transition between phases of different quantized transport. In an outlook I will discuss the extension of the composite approach to topological properties of self-bound many-particle states in 2D lattices.

References
[1] M. Jurgensen, S. Mukherjee, and M. C. Rechtsman, Quantized nonlinear Thouless pumping, Nature
596, 63 (2021)
[2] M. Jurgensen, S. Mukherjee, C. Jorg, and M. C. Rechtsman, Quantized fractional Thouless pumping
of solitons, Nature Physics 19, 420 (2023)
[3] Julius Bohm, Hugo Gerlitz, Christina Jorg, and Michael Fleischhauer Quantum theory of fractional
topological pumping of lattice solitons, arxiv:2506.00090