Defect generation in a spin-1/2 transverse XY chain 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/tau) is quenched repeatedly between -infinity and +infinity. A single passage from h ->-infinity to h ->+infinity 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 -infinity; in the case of an odd number of half periods, the dynamics is stopped at h ->+infinity. The density of defects produced due to the nonadiabatic transitions is calculated by mapping the many-particle system to an equivalent Landau-Zener problem and is generally found to vary as 1/root tau for large tau; 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/root tau for large tau for any number of half periods, and shows an increase in kink density for small tau for an even number; the entropy shows qualitatively the same behavior for any number of half periods. The probability of nonadiabatic transitions and the local entropy saturate to 1/2 and ln 2, respectively, for a large number of repeated quenching.

Publication
PHYSICAL REVIEW B 77, (2008).
Date
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