Quantum mechanics

Electric field

Mathematical optimization

Limit (mathematics)

Hamiltonian (control theory)

Spins

Statistical physics

Anderson localization

Physics

Bloch oscillations

Mathematics

Fermion

Work (physics)

Condensed matter physics

Mathematical analysis

Ergodic theory

Thermalisation

Proceedings of the National Academy of Sciences

In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier-Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.

From Bloch oscillations to many-body localization in clean interacting systems