Local supersolid in moir\'e modulated Bose-Hubbard model using density-matrix renormalization group method

Abstract

The search and characterization of supersolid phases remain a central topic in condensed matter physics. Inspired by the experimental discovery of local superfluid and insulating phases in two-dimensional moir\'e optical lattices [Meng et al., Nature 615, 231 (2023)], we systematically explore the emergence of a local supersolid ($l$SS) phase in a one-dimensional Bose-Hubbard model subjected to a moir\'e potential, using the density-matrix renormalization group method. We impose a maximum site occupation $n_{\rm max}=2$ to realize the soft-core boson constraint. In the absence of nearest-neighbor repulsion, we identify the conventional superfluid, local superfluid, Mott insulator, and moir\'e-induced insulator phases. When the nearest-neighbor repulsion is turned on, the $l$SS phase emerges in the strong-moir\'e regime. This phase is uniquely characterized by three key signatures: (i) coexisting local staggered density order and local off-diagonal coherence within isolated moir\'e supercells; (ii) exponentially decaying global off-diagonal correlations; and (iii) a vanishing global structure factor in the thermodynamic limit, while the local structure factor remains finite. These features clearly distinguish the $l$SS from the conventional global supersolid (SS) phase, which exhibits algebraic correlations and a finite global structure factor. Our results provide a complete microscopic picture of local quantum phases in moir\'e lattices and offer clear experimental observables for detecting $l$SS states with ultracold atoms.