Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation

TL;DR

This paper investigates the dynamics of a quantum Ising chain under periodic quenches, revealing phenomena like dynamical many-body freezing and the emergence of a slow solitary oscillation due to quantum interference.

Contribution

It provides analytical and numerical analysis of dynamical many-body freezing and the emergence of solitary oscillations in a periodically driven quantum Ising chain.

Findings

Observation of non-monotonic dynamical many-body freezing.

Identification of a slow solitary oscillation dominating long-term response.

Collapse of Floquet spectrum at freezing peaks.

Abstract

We study the real-time dynamics of a quantum Ising chain driven periodically by instantaneous quenches of the transverse field (the transverse field varying as rectangular wave symmetric about zero). Two interesting phenomena are reported and analyzed: (1) We observe dynamical many-body freezing or DMF (Phys. Rev. B, vol. 82, 172402, 2010), i.e. strongly non-monotonic freezing of the response (transverse magnetization) with respect to the driving parameters (pulse width and height) resulting from equivocal freezing behavior of all the many-body modes. The freezing occurs due to coherent suppression of dynamics of the many-body modes. For certain combination of the pulse height and period, maximal freezing (freezing peaks) are observed. For those parameter values, a massive collapse of the entire Floquet spectrum occurs. (2) Secondly, we observe emergence of a distinct solitary oscillation with a single frequency, which can be much lower than the driving frequency. This slow oscillation, involving many high-energy modes, dominates the response remarkably in the limit of long observation time. We identify this slow oscillation as the unique survivor of destructive quantum interference between the many-body modes. The oscillation is found to decay algebraically with time to a constant value. All the key features are demonstrated analytically with numerical evaluations for specific results.