Quantum information scrambling in adiabatically-driven critical systems

TL;DR

This paper explores how quantum information, especially symmetry-breaking information, becomes scrambled in adiabatically driven critical quantum systems, revealing mechanisms of information spreading during slow evolutions.

Contribution

It extends quantum information scrambling concepts to adiabatic processes in critical systems and analyzes the underlying mechanisms and effects of scrambling in such scenarios.

Findings

Information is scrambled even in perfect adiabatic evolutions.

Scrambling relates to ground- and excited-state quantum phase transitions.

Perturbations hinder information retrieval, as shown by Loschmidt echo and OTOCs.

Abstract

Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum many-body systems, and has been typically studied in a sudden quench scenario. Here, we extend the notion of quantum information scrambling to critical quantum many-body systems undergoing an adiabatic evolution. In particular, we analyze how the symmetry-breaking information of an initial state is scrambled in adiabatically driven integrable systems, such as the Lipkin--Meshkov--Glick and quantum Rabi models. Following a time-dependent protocol that drives the system from symmetry-breaking to a normal phase, we show how the initial information is scrambled, even for perfect adiabatic evolutions, as indicated by the expectation value of a suitable observable. We detail the underlying mechanism for quantum information scrambling, its relation to ground- and excited-state quantum phase transitions, and quantify the degree of scrambling in terms of the number of eigenstates that participate in the encoding of the initial symmetry-breaking information. While the energy of the final state remains unaltered in an adiabatic protocol, the relative phases among eigenstates are scrambled, and so is the symmetry-breaking information. We show that a potential information retrieval, following a time-reversed protocol, is hindered by small perturbations, as indicated by a vanishingly small Loschmidt echo and out-of-time-ordered correlators. The reported phenomenon is amenable for its experimental verification, and may help in the understanding of information scrambling in critical quantum many-body systems.