Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.Moiré related physics in twisted bilayer two-dimensional (2D) materials has attracted widespread interest in condensed matter physics. Simulation of moiré related physics in cold atom platform is expected to outperform the 2D materials thanks to its advantage of higher tunablility. Here, we demonstrate that, the cold atom platform enables a new mechanism of moiré lattice formation, induced by interlayer interaction with intrinsic "dynamical" character, in contrast to conventional moiré lattice induced by "static" ways such as single-particle interlayer tunneling. Specifically, we consider a twisted bilayer Bose-Hubbard model with vanishing interlayer tunneling, and the bilayer is solely coupled through interlayer interaction that originates from contact interaction of atoms. We find that this system hosts a plethora of novel phases unique to this dynamical lattice, including a variety of Mott insulator (MI) and superfluid (SF) phases either preserving or breaking moiré lattice symmetry, phases with one layer in SF and the other in MI, "interlocked" MI, and self-localized phases at commensurate twist angles, which exhibits the characteristics of Bose glass and quasi-many-body localization in the absence of (quasi)disorder or quasicrystalline lattices. Our prediction can be readily observed in current experimental setup of twisted bilayer optical lattices, opening up new avenues for exploring the rich physics of interaction induced moiré systems in cold atoms.

arXiv:2405.20732Physical Review AJun 3, 20259 citations

Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices

Ivan Dutta, Anamitra Mukherjee, Onur Erten +1 more

Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer ${\mathbb{Z}}_{2}$ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by ${C}_{3z}$ and ${C}_{6z}$ of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer ${\mathbb{Z}}_{2}$ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by ${C}_{3z}$ and ${C}_{6z}$ of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.

arXiv:2506.04181Physical review. B./Physical review. BNov 19, 20250 citations

Frontiers in Synthetic Moiré Quantum Matter

Board on Physics and Astronomy, Division on Engineering and Physical Sciences, National Academies of Sciences, Engineering, and Medicine

National Academies Press eBooksDec 12, 20220 citations

Moiré droplet of ultracold Bose gases in a twisted-bilayer optical lattice

Tianqi Luo, Jing Zhang, Xiaoling Cui

We report the emergence of Moiré droplet in two-dimensional ultracold bosons subjected to a spin-dependent optical lattice, effctively realizing a twisted-bilayer configuration. We show that the droplet formation dramatically enhances the visibility of Moiré pattern in the density profile, even for exceptionally weak lattice potentials. The Moiré pattern can be enhanced similarly by increasing the lattice depth, which, however, also induces droplet diffusion characterized by a spreading density profile. Furthermore, we demonstrate a dynamical generation of Moiré pattern by dragging a small droplet through a moving lattice. At appropriate velocities, the droplet undergoes bifurcation and exhibits pronounced Moiré pattern within periodic time intervals. Our results establish the ultracold droplet as a compelling platform for simulating interacting Moiré physics, particularly the interplay between Moiré lattice and bound-state formation.We report the emergence of Moiré droplet in two-dimensional ultracold bosons subjected to a spin-dependent optical lattice, effctively realizing a twisted-bilayer configuration. We show that the droplet formation dramatically enhances the visibility of Moiré pattern in the density profile, even for exceptionally weak lattice potentials. The Moiré pattern can be enhanced similarly by increasing the lattice depth, which, however, also induces droplet diffusion characterized by a spreading density profile. Furthermore, we demonstrate a dynamical generation of Moiré pattern by dragging a small droplet through a moving lattice. At appropriate velocities, the droplet undergoes bifurcation and exhibits pronounced Moiré pattern within periodic time intervals. Our results establish the ultracold droplet as a compelling platform for simulating interacting Moiré physics, particularly the interplay between Moiré lattice and bound-state formation.

arXiv:2609.28913Sep 24, 20260 citations

{\mathbb{Z}}_{2}

fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by

{C}_{3z}

and

{C}_{6z}

of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.