Quench dynamics of quasi-periodic systems exhibiting Rabi oscillations of two-level integrals of motion

TL;DR

This paper investigates the quench dynamics of a quasi-periodic system with localized integrals of motion, revealing the role of two-level systems in the short-time behavior near the localization transition.

Contribution

It explicitly identifies strongly localized two-level systems as key l-bits influencing dynamics in a quasi-periodic model, advancing understanding of MBL phenomena.

Findings

Localized two-level systems dominate short-time dynamics

Existence of nearly free l-bits in strong disorder regime

Initial state choice affects dynamics near the transition

Abstract

The elusive nature of localized integrals of motion (or l-bits) in disordered quantum systems lies at the core of some of their most prominent features, i.e. emergent integrability and lack of thermalization. Here, we study the quench dynamics of a one-dimensional model of spinless interacting fermions in a quasi-periodic potential with a localization-delocalization transition. Starting from an unentangled initial state, we show that in the strong disorder regime an important subset of the $l$-bits can be explicitly identified with strongly localized two-level systems, associated with particles confined on two lattice sites. The existence of such subsystems forming an ensemble of nearly free l-bits is found to dominate the short-time dynamics of experimentally relevant quantities, such as the Loschmidt echo and the particle imbalance. We investigate the importance of the choice of the initial state by developing a second quench protocol, starting from the ground-state of the model at different initial disorder strengths and monitoring the quench dynamics close to the delicate ETH-MBL transition regime.