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Title:	Critical quench dynamics of random quantum spin chains: ultra-slow relaxation from initial order and delayed ordering from initial disorder
Authors:	Roósz, Gergö;Lin, Yu-Cheng;Iglói, Ferenc 林瑜琤
Contributors:	應物所
Date:	2017-02
Issue Date:	2017-06-23 17:29:04 (UTC+8)
Abstract:	By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, $\\overline{m}(t)$, of the random transverse-field Ising chain after global quenches. We observe different relaxation behaviors for quenches starting from different initial states to the critical point. Starting from a fully ordered initial state, the relaxation is logarithmically slow described by $\\overline{m}(t)\\sim {\\mathrm{ln}}^{a}t$, and in a finite sample of length L the average magnetization saturates at a size-dependent plateau ${\\overline{m}}_{p}(L)\\sim {L}^{-b};$ here the two exponents satisfy the relation $b/a=\\psi =1/2$. Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until $t={t}_{{\\rm{d}}}$ with $\\mathrm{ln}{t}_{{\\rm{d}}}\\sim {L}^{\\psi }$ and then starts to increase until it saturates to an asymptotic value ${\\overline{m}}_{p}(L)\\sim {L}^{-b^{\\prime} }$, with $b^{\\prime} \\approx 1.5$. For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable $\\mathrm{ln}t/{L}^{\\psi }$. Furthermore, the distribution of long-time limiting values of the magnetization shows that the typical and the average values scale differently and the average is governed by rare events. The non-equilibrium dynamical behavior of the magnetization is explained through semi-classical theory.
Relation:	New Journal of Physics,19 , 023055
Data Type:	article
DOI link:	http://dx.doi.org/10.1088/1367-2630/aa60e6
DOI:	10.1088/1367-2630/aa60e6
Appears in Collections:	[Graduate Institute of Applied Physics] Periodical Articles

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