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.
Highlights
The constant progress in manipulating cold atomic gases has provided insight into the non-equilibrium dynamics of isolated, interacting quantum many-body systems
As we show in the following, for most choices of the initial state — as long as g is not too close to the critical point gc = 1 — the approximation above successfully describes the early stages of the dynamics
In this work we reported on a viable approach to study the dynamics of a quenched interacting quantum spin chain with long-range interactions, which originates from the perturbation of a one-dimensional quantum Ising model
Summary
The constant progress in manipulating cold atomic gases has provided insight into the non-equilibrium dynamics of isolated, interacting quantum many-body systems. In order to probe the relaxation of quantum manybody systems, the protocol known as quantum quench has provided a convenient conceptual framework, widely employed in recent investigations[13,14] It consists in suddenly changing a parameter of the many-body Hamiltonian (magnetic field, interaction strength, or coupling among spins, etc) on time scales short enough to leave the system initially frozen in the ground state of the prequench Hamiltonian. Afterwards, on time scales which depend on the strength of the interaction, the effect of quasi-particle scattering becomes relevant and drives the system towards an eventual, bona fide thermalization This mechanism is usually referred to as prethermalization (or as prerelaxation when, instead, the perturbation breaks non-abelian integrability into integrability45), and, this notion was firstly employed in the context of high-energy quantum field theories[46], during the last few years it has been extended to the domain of condensed matter physics. Despite the diversity of approaches developed in order to tackle the quench dynamics of this system, we think it is worth reporting here in full detail our approach, since it suggests that in certain cases pre-thermalization in interacting systems can be understood as the dynamics of an approximate integrable model, which emerges at intermediate time scales and which is not perturbatively connected to the pre-quench model
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