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

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 gc, 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.

Coherent and dissipative dynamics at quantum phase transitions

“…As clearly visible, the function Σ 0 (g i , g) presents a nonanalytic behavior in correspondence of the QCP at g c = 1. Indeed, we have that [575] lim…”

“…However, as argued in Refs. [575,[676][677][678][679][680], some signatures may emerge as well. In particular, integrable many-body systems (such as those mappable into generic noninteracting fermionic systems) develop peculiar discontinuities even in the asymptotic stationary states arising from the quantum quenches [575,676,677].…”

“…[575,[676][677][678][679][680], some signatures may emerge as well. In particular, integrable many-body systems (such as those mappable into generic noninteracting fermionic systems) develop peculiar discontinuities even in the asymptotic stationary states arising from the quantum quenches [575,676,677]. On the other hand, local observables are not expected to present singularities in nonintegrable systems where generic quantum quenches lead to thermalization, since they are generally smooth functions of the temperature (exceptions to this general behavior are seen to emerge in integrable models and in the presence of localization phenomena).…”

“…The above issue related to hard quenches has been thoroughly investigated within the quantum XY model (7), under quenches of the Hamiltonian parameter g driving the transition that separates the quantum paramagnetic and ferromagnetic phases [16,561,562,575,676], starting from the ground states associated with initial values g i . In the thermodynamic limit, the out-of-equilibrium evolution of the energy density [676], and the longitudinal and transverse magnetizations [575], develop a singular dependence on the quench parameter g, or w ≡ g − g c , around the critical value g = g c , for any anisotropy parameter γ > 0 and starting point g i , including the extremal ones corresponding to fully disordered and ordered initial states.…”

Impact of Dissipation on Universal Fluctuation Dynamics in Open Quantum Systems

“…Such open quantum systems have attracted many theoretical and experimental researchers in recent years, and nontrivial consequences of dissipation have been uncovered in a variety of quantum phenomena. In particular, universal dynamics has been extensively explored from various viewpoints such as measurement-induced phase transitions [5][6][7][8][9][10][11][12][13][14][15][16], selforganized criticality [17][18][19], and non-equilibrium phase transitions [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Open quantum systems have thus become a novel playground for studying universal quantum non-equilibrium phenomena.…”