Mobility edge of Stark many-body localization

The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from “extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations) to “localized" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder – if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using “quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.

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Many-Body Localization and the Emergence of Quantum Darwinism

Entropy ◽

10.3390/e23111377 ◽

2021 ◽

Vol 23 (11) ◽

pp. 1377

Author(s):

Nicolás Mirkin ◽

Diego A. Wisniacki

Keyword(s):

Quantum System ◽

Entanglement Entropy ◽

Redundant Information ◽

Many Body ◽

Initial State ◽

Mobility Edge ◽

Critical Degree ◽

Quantum Darwinism ◽

Effect Of Disorder ◽

The Many

Quantum Darwinism (QD) is the process responsible for the proliferation of redundant information in the environment of a quantum system that is being decohered. This enables independent observers to access separate environmental fragments and reach consensus about the system’s state. In this work, we study the effect of disorder in the emergence of QD and find that a highly disordered environment is greatly beneficial for it. By introducing the notion of lack of redundancy to quantify objectivity, we show that it behaves analogously to the entanglement entropy (EE) of the environmental eigenstate taken as an initial state. This allows us to estimate the many-body mobility edge by means of our Darwinistic measure, implicating the existence of a critical degree of disorder beyond which the degree of objectivity rises the larger the environment is. The latter hints the key role that disorder may play when the environment is of a thermodynamic size. At last, we show that a highly disordered evolution may reduce the spoiling of redundancy in the presence of intra-environment interactions.

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