2017/09/30 by Sourav Nandy, K. Sengupta, Arnab Sen · 1 citation
Physics and Astronomy · #cond-mat.str-el
paper · pdf · doi:10.1088/1751-8121/aaced6
published as J. Phys. A: Math. Theor. 51 (2018) 334002 · v2; two-column format, 19 pages, 16 figures (Shortened abstract due to character limit for arXiv submission; see main text); slightly modified version submitted for review
arxiv created 2017/10/31 · arxiv updated 2018/07/13
We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent α. Starting from an initial unentangled state, we show that all local quantities relax to well-defined steady state values in the thermodynamic limit and after n ≫ 1 drive cycles for any α and driving frequency ω. We introduce a distance measure, Dl(n), that characterizes the approach of the reduced density matrix of a subsystem of l sites to its final steady state. We chart out the n dependence of \mathcal Dl(n) and identify a critical value α=αc below which they generically decay to zero as (ω/n)1/2. For α> αc, in contrast, \mathcal Dl(n) ∼ (ω/n)3/2[(ω/n)1/2] for ω→ ∞ [0] with at least one intermediate dynamical transition. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing n for such systems. We point out existence of qualitatively new features in the space-time dependence of mutual information for ω< ω(1)c, where ω(1)c is the largest critical frequency for the dynamical transition for a given α. One such feature is the presence of \it multiple light cone-like structures which persists even when α is large. We also show that the nature of space-time dependence of the mutual information of long-ranged Hamiltonians with α≤ 2 differs qualitatively from their short-ranged counterparts with α> 2 for any drive frequency and relate this difference to the behavior of the Floquet group velocity of such driven system.