Critical quench dynamics of random quantum spin chains: ultra-slow relaxation from initial order and delayed ordering from initial disorder. (28th February 2017) - Roósz, Gergö; Lin, Yu-Cheng; Iglói, Ferenc
Abstract: By means of free fermionic techniques combined with multiple precision arithmetic we study the time evolution of the average magnetization, 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 m ̄ ( t ) ∼ ln a t, and in a finite sample of length L the average magnetization saturates at a size-dependent plateau m ̄ p ( L ) ∼ L − b ; here the two exponents satisfy the relation b / a = ψ = 1 / 2 . Starting from a fully disordered initial state, the magnetization stays at zero for a period of time until t = t d with ln t d ∼ L ψ and then starts to increase until it saturates to an asymptotic value m ̄ p ( L ) ∼ L − b ′, with b ′ ≈ 1.5 . For both quenching protocols, finite-size scaling is satisfied in terms of the scaled variable ln t / L ψ . 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.