1301.5904 (Kai He et al.)

Initial state dependence of the quench dynamics in integrable quantum
systems. III. Chaotic states    [PDF]

Kai He, Marcos Rigol

We study sudden quantum quenches in which the initial states are selected to be either eigenstates of an integrable Hamiltonian, which is non-mappable to a noninteracting one, or a nonintegrable Hamiltonian while the Hamiltonian after the quench is always integrable (and mappable to a noninteracting one). By studying weighted energy densities and entropies, we show that quenches starting from the nonintegrable (chaotic) eigenstates lead to an "ergodic" sampling of the eigenstates of the final Hamiltonian, while those starting from the integrable eigenstates do not (at least for the system sizes accessible to us). This goes in parallel with the fact that the distribution of conserved quantities in the initial states is thermal in the nonintegrable cases and nonthermal in the integrable ones, and means that, in general, thermalization occurs in integrable systems when the quench starts from an eigenstate of a nonintegrable Hamiltonian (away from the edges of the spectrum), while it fails (or requires much larger system sizes) for quenches starting at integrable points that are non-mappable to free models. We test those conclusions by studying the momentum distribution function of hard-core bosons after a quench.

View original: http://arxiv.org/abs/1301.5904