Dynamics after quenches in one-dimensional quantum Ising-like systems

TL;DR

This paper investigates the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems after sudden parameter quenches, analyzing quantum transition signatures, finite-size effects, dissipation impacts, and the persistence of certain dynamical features under integrability breaking.

Contribution

It provides a comprehensive analysis of post-quench dynamics, including the emergence of singularities, finite-size scaling laws, effects of dissipation, and robustness of features when integrability is broken.

Findings

Singularities in infinite-size limit relate to quantum criticality.

Finite systems show power-law scaling and revival phenomena.

Dissipation suppresses key dynamical features.

Abstract

We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter $g$ driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of $g$ around the critical value $g_c$, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of $g$. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.