Initial-state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states

摘要

We study sudden quantum quenches in which the initial states are selected to be either eigenstates of annintegrable Hamiltonian that is nonmappable to a noninteracting one or a nonintegrable Hamiltonian, while thenHamiltonian after the quench is always integrable and mappable to a noninteracting one. By studying weightednenergy densities and entropies, we show that quenches starting from nonintegrable (chaotic) eigenstates leadnto an “ergodic” sampling of the eigenstates of the final Hamiltonian, while those starting from the integrableneigenstates do not (or at least it is not apparent for the system sizes accessible to us). This goes in parallel withnthe fact that the distribution of conserved quantities in the initial states is thermal in the nonintegrable cases andnnonthermal in the integrable ones, and means that, in general, thermalization occurs in integrable systems whennthe quench starts form an eigenstate of a nonintegrable Hamiltonian (away from the edges of the spectrum),nwhile it fails (or requires larger system sizes than those studied here to become apparent) for quenches starting atnintegrable points.We test those conclusions by studying the momentum distribution function of hard-core bosonsnafter a quench.