Defect generation in a spin-12transverseXYchain under repeated quenching of the transverse field

Abstract

We study the quenching dynamics of a one-dimensional spin-1/2 XY model in a transverse field when the transverse field h(= t/τ ) is quenched repeatedly between −∞ and +∞. A single passage from h → −∞ to h → +∞ or the other way around is referred to as a half-period of quenching. For an even number of half-periods, the transverse field is brought back to the initial value of −∞; in the case of an odd number of half-periods, the dynamics is stopped at h → +∞. The density of defects produced due to the non-adiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as 1/ √ τ for large τ ;however, the magnitude is found to depend on the number of half-periods of quenching. For two successive half-periods, the defect density is found to decrease in comparison to a single half-period, suggesting the existence of a corrective mechanism in the reverse path. A similar behavior of the density of defects and the local entropy is observed for repeated quenching. The defect density decays as 1/ √ τ for large τ for any number of half-periods, and shows a increase in kink density for small τ for an even number; the entropy shows qualitatively the same behavior for any number of half-periods. The probability of non-adiabatic transitions and the local entropy saturate to 1/2 and ln 2, respectively, for a large number of repeated quenching.

Nonequilibrium quantum phase transitions in the Ising model

“…Rather recently, a formalism has been developed to deal with this kind of dynamical situation [14,[26][27][28]. The idea is based on the fact that Hamiltonian equation (3) conserves momentum and parity.…”

“…In particular, as a consequence of a generalized parity in the extended Hilbert space [20], under the effect of periodic driving the tunneling can be slowed down or totally suppressed in a perfect coherent way, a phenomenon commonly referred to as coherent destruction of tunneling (CDT) [24,25]. Rather recently, the extension of this concept to manybody systems has been addressed in the context of the Mott-insulator-superfluid transition in ultracold systems both theoretically [13] as well as experimentally [15], and in a two-mode Bose-Hubbard model with time-dependent self-interaction strength [11].The dynamics of one-dimensional spin chains has been addressed extensively when the system is driven slowly through the critical point [26][27][28], where there is a diverging relaxation time and correlation length, and the dynamics cannot be adiabatic in the thermodynamic limit. As a consequence of this, the final state of the system consists of ordered domains whose finite size depend upon the velocity of the parameter variation [29].…”

“…The dynamics of one-dimensional spin chains has been addressed extensively when the system is driven slowly through the critical point [26][27][28], where there is a diverging relaxation time and correlation length, and the dynamics cannot be adiabatic in the thermodynamic limit. As a consequence of this, the final state of the system consists of ordered domains whose finite size depend upon the velocity of the parameter variation [29].…”

Defect Production Due to Quenching Through a Multicritical Point and Along a Gapless Line

“…Let us briefly mention a few other interesting variants of the transverse quenching scheme. In a repeated quenching dynamics of the same model, the transverse field h(= t/τ) is quenched repeatedly between −∞ and +∞ [25]. We refer to a single passage from h → −∞ to h → +∞ or the other way around as a half-period of quenching.…”

“…The non-equilibrium dynamics of a quantum system when quenched very fast [3] or slowly across a quantum critical point [4,5] has attracted the attention of several groups recently. The possibility of experimental realizations of quantum dynamics in spin-1 Bose condensates [6] and atoms trapped in optical lattices [7,8] has led to an upsurge in studies of related theoretical models [3,4,5,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,28,29,30,31,32,33].…”