Entanglement spreading and oscillation. (24th May 2019)

• Record Type: Journal Article
• Authors: Nishida, Mitsuhiro; Nozaki, Masahiro; Sugimoto, Yuji; Tomiya, Akio
• Is Part Of: Journal of statistical mechanics. (2019:May)
• Publication Date: 2019-05-24
• Subjects: 1 -- 2; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ab14d9
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: We study dynamics of quantum entanglement in smooth global quenches with a finite rate, by computing the time evolution of entanglement entropy in 1 + 1 dimensional free scalar theory with time-dependent masses which start from a nonzero value at early time and either crosses or approaches zero. The time-dependence is chosen so that the quantum dynamics is exactly solvable. If the quenches asymptotically approach a critical point at late time, the early-time and late-time entropies are proportional to the time and subsystem size respectively. Their proportionality coefficients are determined by scales: in a fast limit, an initial correlation length; in a slow limit, an effective scale defined when adiabaticity breaks down. If the quenches cross a critical point, the time evolution of entropy is characterized by the scales: the initial correlation length in the fast limit and the effective correlation length in the slow limit. The entropy oscillates, and the entanglement oscillation comes from a coherence between right-moving and left-moving waves if we measure the entropy after time characterized by the quench rate. The periodicity of the late-time oscillation is consistent with the periodicity of the oscillation of zero modes which are zero-momentum value of two point functions of a fundamental field and its conjugate momentum.