Detecting a many-body mobility edge with quantum quenches

TL;DR

This paper proposes a method using quantum quenches to detect many-body mobility edges, demonstrating a dynamical transition in a spinless fermion chain with potential experimental applications.

Contribution

It introduces quantum-quench spectroscopy as a new approach to identify many-body mobility edges in disordered quantum systems.

Findings

Numerical evidence of a many-body mobility edge in a spinless fermion chain.

Identification of a dynamical transition post-quench related to the mobility edge.

Potential for experimental observation using cold-atom setups.

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.