Non-equilibrium quench dynamics in quantum quasicrystals

Abstract

We study the non-equilibrium dynamics of a quasiperiodic quantum Ising chain after a sudden change in the strength of the transverse field at zero temperature. In particular, we consider the dynamics of the entanglement entropy and the relaxation of the magnetization. The entanglement entropy increases with time as a power law, and the magnetization is found to exhibit stretchedexponential relaxation. These behaviors are explained in terms of anomalously diffusing quasiparticles, which are studied in a wave packet approach. The nonequilibrium magnetization is shown to have a dynamical phase transition.

Nonequilibrium quantum relaxation across a localization-delocalization transition

“…For t < ℓ/v max , where v max is some maximal velocity of quasi-particles, the entanglement entropy increases linearly: S ℓ (t) ∼ t; while for t > ℓ/v max , its saturates as S ℓ (t) ∼ ℓ. For random quantum spin chains, due to localized excitations the entanglement entropy saturates at a finite value, except at the critical point, where there is an ultra-slow increase of the form 82 : S ℓ (t) ∼ ln ln t. In the one-dimensional Fibonacci quasi-crystal, where the spectrum of excitations is singular continuous 96 , the entropy grows in a power-law form: S ℓ (t) ∼ t σ , with 0 < σ < 1 being a function of the quench parameters 98 . Another observable we calculate is the local order-parameter (magnetization), m l (t), at a position l in an open chain.…”

“…In the onedimensional Fibonacci quasi-crystal the relaxation of the bulk magnetization is given in a stretched-exponential form 98 : m b (t) ∼ exp(−C/t µ ). Here the exponent µ and the exponent of the entanglement entropy, σ, are found to be close to each other, at least in the so called non-oscillatory phase.…”

“…[98]. In this region of the chain the local magnetization is practically independent of l and we consider it as the bulk magnetization and will be denoted by m b (t).…”

Quantum quench dynamics of the Coulomb Luttinger model

“…Other relevant and interesting aspects that arise are related to the dynamics after the quench in connection to the so called 'light-cone effect' 8,9 . These aspects of the non-equilibirum dynamics after a quantum quench have been investigated in various specific models such as the quantum Ising chain [10][11][12][13][14] , one dimensional (1D) bosonic models [15][16][17][18] , the sineGordon [19][20][21] , and the Luttinger model (LM) 22,23 . General results have been obtained from theoretical investigations involving conformal field theory (CFT) 9,24,25 .…”

Non-equilibrium dynamics of one-dimensional isolated quantum systems

“…With the results of Ref. [176]) (see equation (16)) the long-time limiting value of the surface magnetization, m s p , can be calculated exactly:…”