We study the unitary dynamics and the thermalization properties of free-fermion-like Hamiltonians after a sudden quantum quench, extending the results of S. Ziraldo et al. [ Phys. Rev. Lett. 109 247205 (2012)]. With analytical and numerical arguments, we show that the existence of a stationary state and its description with a generalized Gibbs ensemble (GGE) depend crucially on the observable considered (local versus extensive) and on the localization properties of the final Hamiltonian. We present results on two one-dimensional (1D) models, the disordered 1D fermionic chain with long-range hopping and the disordered Ising/XY spin chain. We analytically prove that, while time averages of one-body operators are perfectly reproduced by GGE (even for finite-size systems, if time integrals are extended beyond revivals), time averages of many-body operators might show clear deviations from the GGE prediction when disorder-induced localization of the eigenstates is at play.
|Titolo:||Relaxation and thermalization after a quantum quench: Why localization is important|
|Autori:||Ziraldo, S.; Santoro, G.E.|
|Rivista:||PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.1103/PhysRevB.87.064201|
|Appare nelle tipologie:||1.1 Journal article|