Prethermalization from a low-density Holstein-Primakoff expansion

Abstract

We consider the non-equilibrium dynamics arising after a quench of the transverse magnetic field of a quantum Ising chain, together with the sudden switch-on of a long-range interaction term. The dynamics after the quantum quench is mapped onto a fully-connected model of hard-core bosons, after a suitable combination of a Holstein-Primakoff transformation and of a low-density expansion in the quasi-particles injected by the quench. This mapping holds for a broad class of initial states and for quenches which do not cross the critical point of the transverse field Ising model. We then study the algebraic relaxation in time of a number of observables towards a metastable, pre-thermal state, which becomes the asymptotic steady state in the thermodynamic limit.

17 pages, 5 figures; close to published version

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• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Quasiparticle explanation of "weak thermalization" regime under quench in a non-integrable quantum spin chain
• Exact solution for the quench dynamics of a nested integrable system
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State
• Quench dynamics of spin-imbalanced Fermi-Hubbard model in one dimension