Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge
Phys. Rev. Lett. 122, 170403
![Figure 3
Power-law exponents: Measured relaxation exponents as a function of the detuning strength for the GAA model at U/J0=1. The error bars denote the uncertainty of the fit. The blue shaded region shows the result of numerical simulations including fit uncertainties, while the brown shaded area indicates a regime of slow dynamics with finite relaxation exponents reminiscent of the slow dynamics observed in the interacting AA model [50]. The lower part of the figure represents the situation in the noninteracting system which exhibits an extended and a localized phase as well as a single-particle intermediate phase whose numerically predicted width [51] is represented by the gray shaded region.](/36155/original-1562054309.jpg?t=eyJ3aWR0aCI6MzQxLCJmaWxlX2V4dGVuc2lvbiI6ImpwZyIsIm9ial9pZCI6MzYxNTV9--a01054cfc6b9963950c00db50e69c94247ea752a "Figure 3
Power-law exponents: Measured relaxation exponents as a function of the detuning strength for the GAA model at U/J0=1. The error bars denote the uncertainty of the fit. The blue shaded region shows the result of numerical simulations including fit uncertainties, while the brown shaded area indicates a regime of slow dynamics with finite relaxation exponents reminiscent of the slow dynamics observed in the interacting AA model [50]. The lower part of the figure represents the situation in the noninteracting system which exhibits an extended and a localized phase as well as a single-particle intermediate phase whose numerically predicted width [51] is represented by the gray shaded region.")
![Figure 3
Power-law exponents: Measured relaxation exponents as a function of the detuning strength for the GAA model at U/J0=1. The error bars denote the uncertainty of the fit. The blue shaded region shows the result of numerical simulations including fit uncertainties, while the brown shaded area indicates a regime of slow dynamics with finite relaxation exponents reminiscent of the slow dynamics observed in the interacting AA model [50]. The lower part of the figure represents the situation in the noninteracting system which exhibits an extended and a localized phase as well as a single-particle intermediate phase whose numerically predicted width [51] is represented by the gray shaded region.](/36155/original-1562054309.jpg?t=eyJ3aWR0aCI6MjQ2LCJvYmpfaWQiOjM2MTU1fQ%3D%3D--baec74d12b58bdb97256fc83b31b34efa8b49323)
Figure 3
Power-law exponents: Measured relaxation exponents as a function of the detuning strength for the GAA model at U/J0=1. The error bars denote the uncertainty of the fit. The blue shaded region shows the result of numerical simulations including fit uncertainties, while the brown shaded area indicates a regime of slow dynamics with finite relaxation exponents reminiscent of the slow dynamics observed in the interacting AA model [50]. The lower part of the figure represents the situation in the noninteracting system which exhibits an extended and a localized phase as well as a single-particle intermediate phase whose numerically predicted width [51] is represented by the gray shaded region.
A single-particle mobility edge marks a critical energy separating extended from localized states and characterizes the single-particle intermediate phase of our one-dimensional non-interacting quantum system with a weak quasiperiodic potential. Here, we investigate the corresponding interacting system, where the existence of many-body localization (MBL) and a many-body intermediate phase (MBIP) are still open and heavily debated questions. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL, when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential MBIP.
To view the full publication visit: Phys. Rev. Lett. 122, 170403 (2019)