Abstract
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.
Highlights
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
We investigated systematically the ground-state phase diagram making use of quantum Monte Carlo (QMC) simulations based on the Stochastic Series Expansion formulation [39] as well as on the density-matrix renormalization group (DMRG) [40, 41]
In this paper we have proposed and numerically demonstrated a technique to probe the localized vs. extended nature of selected regions in the spectrum of a strongly disordered, interacting quantum systems
Summary
A fundamental paradigm in classical many-body physics – laying the foundations of statistical mechanics – is that of ergodicity, namely the ability of a many-body system to sample the microcanonical ensemble of states by means of its very own Hamiltonian dynamics [1]. Recent theoretical work challenges the very existence of many-body mobility edges, based on rare-event arguments [28] Another very intriguing aspect concerns the ETH regime close to the transition, which is predicted [29,30] and numerically shown [31] to display a very rich phenomenology, characterized by a disorder- and energy-dependent slow dynamics. The structure of our paper is as follows: Sec. 2 discusses the ground-state phase diagram of the model of one-dimensional interacting spinless fermions in a quasi-periodic potential; Sec. 3 focuses on the properties of the excitation spectrum and the level-statistics, entanglement and fluctuation signatures of the existence of a many-body mobility edge; Sec. 4 discusses the dynamical signatures of the mobility edge as probed via quantum-quench spectroscopy
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