Prethermalization from a low-density Holstein-Primakoff expansion

TL;DR

This paper investigates the non-equilibrium dynamics of a quantum Ising chain with long-range interactions after a quench, revealing algebraic relaxation towards a pre-thermal metastable state using a novel low-density Holstein-Primakoff expansion.

Contribution

It introduces a new mapping of the post-quench dynamics onto a fully-connected bosonic model via a low-density Holstein-Primakoff expansion, applicable to a broad class of initial states.

Findings

Observation of algebraic relaxation towards a pre-thermal state

Mapping of the dynamics onto a fully-connected bosonic model

Identification of conditions for the validity of the mapping

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.