Many-body localization provides a mechanism to avoid thermalization in isolated interacting quantum systems. The breakdown of thermalization may be complete, when all eigenstates in the many-body spectrum become localized, or partial, when the so-called many-body mobility edge separates localized and delocalized parts of the spectrum. Previously, De Roeck et al. [Phys. Rev. B 93, 014203 (2016)] suggested a possible instability of the many-body mobility edge in energy density. The local ergodic regions—so-called “bubbles”—resonantly spread throughout the system, leading to delocalization. In order to study such instability mechanism, in this work we design a model featuring many-body mobility edge in particle density: the states at small particle density are localized, while increasing the density of particles leads to delocalization. Using numerical simulations with matrix product states, we demonstrate the stability of many-body localization with respect to small bubbles in large dilute systems for experimentally relevant timescales. In addition, we demonstrate that processes where the bubble spreads are favored over processes that lead to resonant tunneling, suggesting a possible mechanism behind the observed stability of many-body mobility edge. We conclude by proposing experiments to probe particle density mobility edge in the Bose-Hubbard model.
Physical Review B
Acknowledgments. We acknowledge useful discussions with W. De Roeck and A. Michailidis. P.B. was supported by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 665385. D.A. was supported by the Swiss National Science Foundation. M.S. was supported by European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 850899). This work benefited from visits to KITP, supported by the National Science Foundation under Grant No. NSF PHY-1748958 and from the program “Thermalization, Many Body Localization and Hydrodynamics” at International Centre for Theoretical Sciences (Code: ICTS/hydrodynamics2019/11).
Brighi P, Abanin DA, Serbyn M. Stability of mobility edges in disordered interacting systems. Physical Review B. 2020;102(6). doi:10.1103/physrevb.102.060202
Brighi, P., Abanin, D. A., & Serbyn, M. (2020). Stability of mobility edges in disordered interacting systems. Physical Review B. American Physical Society. https://doi.org/10.1103/physrevb.102.060202
Brighi, Pietro, Dmitry A. Abanin, and Maksym Serbyn. “Stability of Mobility Edges in Disordered Interacting Systems.” Physical Review B. American Physical Society, 2020. https://doi.org/10.1103/physrevb.102.060202.
P. Brighi, D. A. Abanin, and M. Serbyn, “Stability of mobility edges in disordered interacting systems,” Physical Review B, vol. 102, no. 6. American Physical Society, 2020.
Brighi P, Abanin DA, Serbyn M. 2020. Stability of mobility edges in disordered interacting systems. Physical Review B. 102(6), 060202(R).
Brighi, Pietro, et al. “Stability of Mobility Edges in Disordered Interacting Systems.” Physical Review B, vol. 102, no. 6, 060202(R), American Physical Society, 2020, doi:10.1103/physrevb.102.060202.
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