Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge

We study many-body localization (MBL) in the quasiperiodic t₁-t₂ model, focusing on the role of next-nearestneighbor (NNN) hopping t₂, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction U. For weak interactions (U << t₁), this model is always nonthermal. For intermediate interactions (U ∼ t₁), the thermalMBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions (U >> t₁), the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.