Twisted transition metal dichalcogenides offer an exceptionally tunable moiré platform for studying correlation physics beyond conventional condensed matter systems. In particular, the intriguing interplay between the displacement field and the twist angle remains to be fully resolved. In this paper, we use large-scale density matrix renormalization group simulations to study the minimal moiré Hubbard model on a triangular lattice at half-filling, where the displacement field effect is captured by a spin-dependent staggered flux. We find that the displacement field significantly enriches the triangular Hubbard phase diagram in several qualitative ways. It rapidly destabilizes the chiral spin liquid phase beyond a narrow weak-field regime, induces pronounced chiral correlations in the strong-coupling
120∘-antiferromagnetic phase, and stabilizes incommensurate spin-density wave phases at weaker coupling. We further find signatures of a continuous transition between the chiral spin liquid and chiral antiferromagnetic phases at a finite displacement field, potentially driven by spinon condensation. Our results uncover rich displacement-field-driven many-body physics and provide useful guidance for future experiments in moiré superlattice systems.
At
n=3/4 filling of the moiré flat band, transition metal dichalcogenide moiré bilayers will develop kagome charge order. We derive an effective spin model for the resulting localized spins and find that its further neighbor spin interactions can be much less suppressed than the corresponding electron hopping strength. Using density matrix renormalization group simulations, we study its phase diagram and, for realistic model parameters relevant for WSe
2/WS
2, we show that this material can realize the exotic chiral spin liquid phase and the highly debated kagome spin liquid. Our work thus demonstrates that the frustration and strong interactions present in TMD heterobilayers provide an exciting platform to study spin liquid physics.
Motivated by the recent proposal of realizing an SU(4) Hubbard model on triangular moire superlattices, we present a DMRG study of an
SU(4) spin model obtained in the limit of large repulsion for integer filling
νT=1,3. We retain terms in the
t/U expansion up to
O(U2t3) order, that generates nearest-neighbor exchange
J, as well as an additional three-site ring exchange term,
K, which is absent in the SU(2) S=1/2 case. For filling
νT=3, when increasing the three-site ring exchange term
K∼U2t3, we identify three different phases: a spin-symmetric crystal, an
SU(4)1 chiral spin liquid (CSL) and a decoupled one dimensional chain (DC) phase. The CSL phase exists at intermediate coupling:
U/t∈[11.3,22.9]. The sign of
K is crucial to stabilizing the CSL and the DC phase. For filling
νT=1 with the opposite sign of
K, the spin-symmetric crystal phase survives to very large
K. We propose to search for the CSL phase in moire bilayers. For example, in twisted AB stacked transition metal dichalcogenide (TMD) bilayers, the
SU(4) spin is formed by layer pseudospin combined with the real spin (locked to valley). The layer pseudospin carries an electric dipole moment in
z direction, thus the CSL is really a dipole-spin liquid, with quantum fluctuations in both the electric moment and magnetic moment . The CSL phase spontaneously breaks the time reversal symmetry and shows a quantum anomalous Hall effect in spin transport and dipole transport. Smoking gun evidence for the CSL could be obtained through measurement of the quantized dipole Hall effect in counter-flow transport.
Motivated by twisted transition metal dichalcogenides (TMDs), we study an extended Hubbard model with both on-site and off-site repulsive interactions, in which Mott insulating states with concomitant charge order occur at fractional fillings. To resolve the charge ordering as well as the fate of the local moments formed thereby, we perform large-scale density matrix renormalization group calculations on cylindrical geometries for several filling fractions and ranges of interaction strength. Depending on the precise parameter regime, both antiferromagnetically ordered as well as quantum-disordered states are found, with a particularly prominent example being a quantum spin liquid-type ground state on top of charge-ordering with effective Kagomé geometry. We discuss the different mechanisms at play in stabilizing various electronic and magnetic states. The results suggest that moiré TMDs are a promising venue for emergent quantum magnetism of strongly interacting electrons.
Twisted transition metal dichalcogenide (TMD) homobilayers have recently emerged as a powerful platform for studying correlated insulating states. In the strongly correlated limit, we construct an effective spin Hamiltonian on a honeycomb lattice that includes the Heisenberg interaction and nonsymmetric interactions such as a Dzyaloshinskii-Moriya interaction and a Kane-Mele coupling for the Mott-insulating phase at half-filling. For the twisted TMD homobilayers, the spin-orbit coupling in the Hubbard model, which is expected to induce the antisymmetric exchange couplings in the effective spin Hamiltonian, is a highly tunable and experimentally accessible quantity that can be tuned by an applied electric field. In this study, we investigate classical and quantum phase diagrams of the effective spin Hamiltonian using analytical and numerical methods. We show that the model exhibits a rich classical phase diagram including an antiferromagnetic (AFM) phase, a planar spiral ordered phase with high classical degeneracy, a
z-AFM phase, a noncoplanar phase, a noncollinear phase, and a ${120}^{\ensuremath{\circ}}$-AFM phase. In the quantum treatment, we calculate low-energy magnon excitation spectrum, ground-state energy, and static spin structure factor using linear spin-wave theory and density matrix renormalization group methods to compose the quantum phase diagram of the effective spin Hamiltonian. Beyond the Heisenberg interaction, we find that the existence of these antisymmetric couplings is responsible for the quantum spin liquid,
z-AFM, noncoplanar, and ${120}^{\ensuremath{\circ}}$ phases. Twisted TMD homobilayers, therefore, offer rich platforms for realizing rich phases of matter such as quantum spin liquid, noncoplanar, and ${120}^{\ensuremath{\circ}}$, resulting from the spin-orbit coupling.
We propose multi-layer moire structures in strong external magnetic fields as a novel platform for realizing highly-tunable, frustrated Hubbard physics with topological order. Identifying the layer degree of freedom as a pseudo spin, allows us to retain SU(2) symmetry while controlling ring-exchange processes and concurrently quenching the kinetic energy by large external magnetic fields. This way, a broad class of interacting Hubbard-Hofstadter states and their transitions can be studied. Remarkably, in the limit of strong interactions the system becomes Mott insulating and we find chiral pseudo spin liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable towards relevant perturbations. We discuss how layer pseudo-spin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moire systems, our approach provides a promising route towards the experimental realization and control of topologically ordered phases of matter.