Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems (1612.07173v2)

Abstract: In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.

Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems

This paper investigates the many-body localization (MBL) transition in one-dimensional quasiperiodic systems, focusing on the interlinked concepts of localization and thermalization in disordered quantum systems. The paper provides detailed experimental and numerical analyses of the slow dynamics approaching the MBL transition, contributing to the understanding of nonergodic behavior in condensed matter systems.

Overview of the Study

Many-body localization in disordered or quasiperiodic fields prevents an interacting system from reaching thermal equilibrium, distinguishing it from conventional thermalization processes. Unlike conventional quantum phase transitions, the MBL transition occurs over a range of energy densities. This paper emphasizes the slow relaxation of the density imbalance near the MBL transition, corroborated by experiments and numerical simulations in quasiperiodic setups. A significant observation is the gradual slowdown of relaxation dynamics near the transition, analogous to true-random systems.

Methodological Approach

Experimental Setup:

The authors utilize a one-dimensional Fermi-Hubbard model, enhanced by a quasiperiodic potential, to paper the MBL transition. Spinful fermions on a lattice interact under the Aubry-André model dynamics, subject to on-site interactions and deterministic quasiperiodic disorder. The initial state is prepared in a charge-density wave (CDW) pattern, and imbalance measurements track the evolution toward localization.

Numerical Simulations:

Complementing the experiments, exact diagonalization (ED) simulations across systems with various sizes and initial conditions provide insights into the imbalance dynamics, validating the experimental results. Using a 20-site model, the simulations explore longer time scales, capturing both the fast initial decay and the subsequent slow relaxation indicative of MBL behavior.

Key Findings

1. Slow Relaxation Dynamics: The paper presents significant slowing of system relaxation as the system transitions to the MBL phase. The dynamics are consistent with previous findings in true-random disorder systems, suggesting a possible shared microscopic origin.
2. Phase Transition Estimation: Through power-law analyses of the relaxation exponents, the research delineates a lower boundary for the MBL transition in the quasiperiodic system. Despite the presence of finite external bath couplings, critical disorder strength is estimated, offering improved accuracy over previous studies.
3. Experimental and Numerical Correlation: The well-correlated experimental and simulation results underscore the viability of quasiperiodic systems as proxies for studying MBL transitions, circumventing some finite-size limitations inherent in true-random systems.

Implications and Future Directions

This research contributes significant insights into the nature of MBL transitions in quasiperiodic systems, suggesting implications for understanding thermalization barriers in closed quantum systems. The identification of slow dynamics prompts further investigation into the underlying mechanisms, such as state-induced rare regions or atypical transition rates in single-particle states. These findings pave the way for refined experimental setups that could systematically mitigate bath-coupling effects, thereby enhancing the precision of critical point estimations.

Conclusion

This paper provides a nuanced understanding of how MBL emerges in quasiperiodic settings, enriching the theoretical discourse on localization dynamics in many-body systems. Insights from this paper could stimulate future research into nonergodic phenomena, contributing to the growing field of quantum materials science and potential applications in quantum computing and information theory.