Dynamics of Interacting Bosons on the Sawtooth Lattice with a Flat Band

Quantum many-body systems are expected to relax to a thermal state over time, with some exceptions such as systems with atypical eigenstates. In this study, we investigate the effect of the existence of spatially localized eigenstates on the relaxation dynamics of interacting bosons loaded into a one-dimensional sawtooth lattice, which exhibits a flat band in the single-particle spectrum by tuning the hopping rates. Using the time-evolving block decimation algorithm, we simulate the time evolution of the local density profile based on the Bose-Hubbard model with different initial conditions. Our results show the presence of the flat band leads to a significant slowing down of relaxation for weak interactions. Even for strong interaction, when the initial state includes an isolated localized single-particle eigenstate in the superposition, remnants of the initial bias in the density profile persist for a long time. This particular relaxation dynamics can be tested using ultracold atoms in optical lattices.