Many-body localization in clean chains with long-range interactions

Strong long-range interaction leads to localization in a closed quantum system without disorders. Employing the exact diagonalization method, I numerically investigate thermalization and many-body localization in translational invariant quantum chains with finite Coulomb interactions. In the computational basis, excluding all trivial degeneracies, the interaction-induced localization is well demonstrated in aspects of level statistics, eigenstate expectation values, and Anderson localization on graphs constructed of many-body bases. The nature of localization for generic eigenstates is attributed to the quasidisorder from the power-law interactions, and the full localization in the Hilbert space is similar to that in the disorder case. However, due to real-space symmetries, the long-time dynamics is dominated by the degenerated eigenstates and eventually reaches homogeneity in real space. On the other hand, the entanglement entropy exhibits size dependence beyond the area law for the same reason, even deep in the localized state, indicating an incomplete localization in real space. © 2023 American Physical Society.