Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble

Abstract

We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Neel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. Lett. 110, 257203 (2013)], however, we find excellent agreement with the numerical data. We, therefore, conclude that the GGE cannot give a complete description even of local observables, while the quench-action formalism correctly captures the steady state in this case.

5+2 pages, 5 figures. v2: final (published) version

References in corpus (17)

• Thermalization and its mechanism for generic isolated quantum systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• The Luttinger model following a sudden interaction switch-on
• Dephasing and the steady state in quantum many-particle systems
• Strong and weak thermalization of infinite non-integrable quantum systems
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Generalized Thermalization in an Integrable Lattice System
• Effective thermal dynamics following a quantum quench in a spin chain
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Validity of the GGE for quantum quenches from interacting to noninteracting models
• Global large time dynamics and the generalized Gibbs ensemble
• Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
• Closed and Open System Dynamics in a Fermionic Chain with a Microscopically Specified Bath: Relaxation and Thermalization

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