Quantum quenches and thermalization on scale-free graphs

We show that after a quantum quench of theparameter controlling the number of particles in a Fermi–Hubbard model on scale-free graphs, the distribution ofenergy modes follows a power-law dependent on thequenched parameter and the connectivity of the graph. Thispaper contributes to the literature of quantum quenches onlattices, in which, for many integrable lattice models thedistribution of modes after a quench thermalizes to ageneralized Gibbs ensemble; this paper provides anotherexample of distribution which can arise after relaxation.We argue that the main role is played by the symmetry ofthe underlying lattice which, in the case we study, is scalefree, and to the distortion in the density of modes.