Detecting a many-body mobility edge with quantum quenches

• DOI: 10.21468/scipostphys.1.1.010
• Publication Date: 2016-10-27T07:17:37Z
• Authors: Piero Naldesi; Elisa Ercolessi; Tommaso Roscilde
• Keywords: many-body localisation; quantum quench; Quantum Physics; Strongly Correlated Electrons (cond-mat.str-el); Physics; QC1-999; FOS: Physical sciences; Disordered Systems and Neural Networks (cond-mat.dis-nn); Condensed Matter - Disordered Systems and Neural Networks; 01 natural sciences; 7. Clean energy; Condensed Matter - Strongly Correlated Electrons; 0103 physical sciences; Quantum Physics (quant-ph)

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.