Quantum quenches and thermalization on scale-free graphs

TL;DR

This paper investigates how quantum quenches in a Fermi-Hubbard model on scale-free graphs lead to energy mode distributions following a power law, highlighting the influence of lattice symmetry and connectivity on thermalization behavior.

Contribution

It demonstrates that energy mode distributions after a quantum quench on scale-free graphs follow a power law, expanding understanding of relaxation in non-lattice quantum systems.

Findings

Energy mode distributions follow a power law dependent on the quenched parameter and graph connectivity.

The lattice symmetry and mode density distortions significantly influence the relaxation process.

Provides an example of non-thermal distribution arising after quantum relaxation.

Abstract

We show that after a quantum quench of the parameter controlling the number of particles in a Fermi-Hubbard model on scale free graphs, the distribution of energy modes follows a power law dependent on the quenched parameter and the connectivity of the graph. This paper contributes to the literature of quantum quenches on lattices, in which, for many integrable lattice models the distribution of modes after a quench thermalizes to a Generalized Gibbs Ensemble; this paper provides another example of distribution which can arise after relaxation. We argue that the main role is played by the symmetry of the underlying lattice which, in the case we study, is scale free, and to the distortion in the density of modes.