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Optical lattice systems provide exceptional platforms for quantum simulation of many-body systems. We focus on the doubly modulated Bose-Hubbard model driven by both time-dependent on-site energy and interaction, and predict the emergence…
Moir\'e superlattices formed in two-dimensional semiconductor heterobilayers provide a new realization of Hubbard model physics in which the number of electrons per effective atom can be tuned at will. We report on an exact diagonalization…
We study localization driven solely by interparticle interactions in moir\'e lattice systems without intrinsic disorder or externally imposed quasiperiodic potentials. We consider a one-dimensional bilayer with incommensurate lattice…
The emergence of moir\'e materials with flat bands provides a platform to systematically investigate and precisely control correlated electronic phases. Here, we report local electronic compressibility measurements of a twisted…
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact…
In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an {\em octopole} coupling between two neighboring…
The ideal honeycomb lattice, featuring sublattice and SU(2) spin rotation symmetries, is a fundamental model for investigating quantum matters with topology and correlations. With the rise of the moir\'e-based design of model systems,…
Moir\'e superlattices host a rich variety of correlated topological states, including interaction-driven integer and fractional Chern insulators. A common approach to study interacting ground states at integer fillings is the Hartree-Fock…
The moir\'e Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic…
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard…
There is strong interest in discovering or designing wide gap Chern insulators. Here we follow a Chern insulator to trivial Mott insulator transition versus interaction strength U in a honeycomb lattice Fe-based transition metal oxide,…
A major challenge in condensed matter physics is integrating topological phenomena with correlated electron physics to leverage both types of states for next-generation quantum devices. Metal-insulator transitions (MITs) are central to…
We report ten ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice; including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott…
The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and…
Effects of electron correlations on Anderson insulators have been one of the central themes for recent two decades, suggesting that the Anderson insulating phase turns into a novel insulating state referred to as many body localization…
We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various…
We have fabricated an encapsulated monolayer MoS$_{\mathrm{2}}$ device with metallic ohmic contacts through a pre-patterned hBN layer. In the bulk, we observe an electron mobility as high as 3000 cm$^{\mathrm{2}}$/Vs at a density of 7…
Moir\'e superlattices in van der Waals structures can be used to control the electronic properties of the material and lead to emergent correlated and topological phenomena. Its first demonstration in van der Waals magnets exhibited…
For a system at a temperature of absolute zero, all thermal fluctuations are frozen out, while quantum fluctuations prevail. These microscopic quantum fluctuations can induce a macroscopic phase transition in the ground state of a many-body…
Artificially twisted heterostructures of semiconducting transition metal dichalcogenides (TMDs) offer unprecedented control over their electronic and optical properties via the spatial modulation of interlayer interactions and structural…