Entanglement entropy and out-of-time-order correlator in the long-range Aubry-Andr\'e-Harper model

TL;DR

This paper explores the dynamics of entanglement entropy and out-of-time-order correlators in the long-range Aubry-André-Harper model, revealing phase-dependent behaviors and new insights into quasiperiodic systems with long-range hopping.

Contribution

It provides a detailed analysis of entanglement and OTOC dynamics in the long-range AAH model, highlighting phase-specific behaviors and the effects of long-range hopping.

Findings

Logarithmic entanglement growth in mixed phases with long-range hopping.

System size dependence of entanglement saturation varies across phases.

Distinct power-law behaviors of OTOC growth and decay in different phases.

Abstract

We investigate the nonequilbrium dynamics of entanglement entropy and out-of-time-order correlator (OTOC) of noninteracting fermions at half-filling starting from a product state to distinguish the delocalized, multifractal (in the limit of nearest neighbor hopping), localized and mixed phases hosted by the quasiperiodic Aubry-Andr\'e-Harper (AAH) model in the presence of long-range hopping. For sufficiently long-range hopping strength a secondary logarithmic behavior in the entanglement entropy is found in the mixed phases whereas the primary behavior is a power-law the exponent of which is different in different phases. The saturation value of entanglement entropy in the delocalized, multifractal and mixed phases depends linearly on system size whereas in the localized phase (in the short-range regime) it is independent of system size. The early-time growth of OTOC shows very different power-law behaviors in the presence of nearest neighbor hopping and long-range hopping. The late time decay of OTOC leads to noticeably different power-law exponents in different phases. The spatial profile of OTOC and its system-size dependence also provide distinct features to distinguish phases. In the mixed phases the spatial profile of OTOC shows two different dependences on space for small and large distances respectively. Interestingly the spatial profile contains large fluctuations at the special locations related to the quasiperiodicity parameter in the presence of multifractal states.