Novel phases in long-range interacting quantum many-body systems

Understanding quantum phase transitions in low-dimensional systems with long-range interactions lies at the forefront of many-body physics. This work focuses on the ground-state properties of strongly correlated one-dimensional (1D) bosonic systems with power-law hopping, where quantum coherence and collective effects give rise to behaviors fundamentally distinct from those in short-range models. Using exact numerical methods, including Path Integral Monte Carlo and the Worm Algorithm, we investigate both disorder- and interaction-driven localization transitions from superfluid to insulating phases, in systems where hopping decays with distance as 1/r^α. A key result of this study is the discovery of a family of continuous, scale-invariant quantum phase transitions that deviate from the conventional Berezinskii-Kosterlitz-Thouless (BKT) scenario typically expected in 1D. This indicates that long-range hopping leads to a fundamentally different localization mechanism, and we propose a new phase diagram capturing this behavior. Our findings pinpoint the regime α ≤ α∗ = 3 as one where long-range effects dominate—challenging earlier predictions from bosonization and finite-size numerical studies. The results serve as a benchmark for future theoretical efforts and offer quantitative guidance to experimental platforms capable of realizing XY models with long-range couplings, such as dipolar atoms and molecules, Rydberg arrays, and trapped ion chains.