The fate of current, residual energy and entanglement entropy in aperiodic driving of one dimensional Jordan Wigner integrable models

TL;DR

This paper studies how aperiodic driving causes one-dimensional Jordan Wigner integrable models, like the hard-core boson chain and transverse field Ising model, to heat up to infinite temperature and reach thermal equilibrium, with detailed analytical results.

Contribution

It provides an exact analytical framework for understanding the asymptotic thermalization and entanglement dynamics in aperiodically driven integrable models.

Findings

Models heat to infinite temperature with minimal aperiodicity

Initial current vanishes asymptotically in HCB chain

Entanglement reaches thermal value in Ising chain

Abstract

We investigate the dynamics of two Jordan Wigner solvable models, namely, the one dimensional chain of hard-core bosons (HCB) and the one-dimensional transverse field Ising model under coin-toss like aperiodically driven staggered on-site potential and the transverse field, respectively. It is demonstrated that both the models heat up to the infinite temperature ensemble for a minimal aperiodicity in driving. Consequently, in the case of the HCB chain, we show that the initial current generated by the application of a twist vanishes in the asymptotic limit for any driving frequency. For the transverse Ising chain, we establish that the system not only reaches the diagonal ensemble but the entanglement also attains the thermal value in the asymptotic limit following initial ballistic growth. All these findings, contrasted with that of the perfectly periodic situation, are analytically established in the asymptotic limit within an exact disorder matrix formalism developed using the uncorrelated binary nature of the coin-toss aperiodicity.