We propose multilayer moiré 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 pseudospin 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 pseudospin-liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable toward relevant perturbations. We discuss how layer pseudospin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moiré systems, our approach provides a promising route toward the experimental realization and control of topologically ordered phases of matter. Published by the American Physical Society 2024
We propose multilayer moiré 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 pseudospin 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 pseudospin-liquid phases which are induced by the magnetic field. We find that this topologically ordered state remains exceptionally stable toward relevant perturbations. We discuss how layer pseudospin can be probed in near-term experiments. As the magnetic flux can be easily tuned in moiré systems, our approach provides a promising route toward the experimental realization and control of topologically ordered phases of matter. Published by the American Physical Society 2024
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.
As one of the most intriguing states of matter, the chiral spin liquid (CSL) has attracted much scientific interest while its existence and mechanism in crystalline strongly correlated systems remain hotly debated. On the other hand, strong correlation driven emergent phenomena can be realized in twisted transition metal dichalcogenide bilayers with a tremendously tunable large length scale providing a new platform for the emergence of CSLs. We focus on a strongly correlated model relevant to heterobilayer WSe2/MoSe2 and investigate the Mott insulating phase at half filling under an out-of-plane magnetic field. Considering both its orbital and spin Zeeman effects we identify three conventionally ordered phases including a ${120}^{\ensuremath{\circ}}$ N\'eel phase, a stripe phase, and an up-up-down phase. For intermediate fields an emergent quantum spin liquid phase is identified with partial spin polarization. We further characterize its topological nature as the $\ensuremath{\nu}=1/2$ Laughlin CSL through the topological entanglement spectrum and quantized spin pumping under spin flux insertion. In addition, we map out the quantum phase diagram for different twisted angles in an experimentally accessible parameter regime.
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.
Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties and the promise that they hold for realizing elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications.
This thesis investigates quantum magnetism in two-dimensional synthetic systems, where strong correlations, geometric frustration, and enhanced quantum fluctuations produce unconventional magnetic phases. I focus on two major classes of engineered platforms: moiré materials and quantum simulators, which offer precise control over lattice geometry, interaction strengths, and dynamics, enabling access to regimes beyond conventional condensed-matter approaches. The first project studies moiré magnetism in strained multilayers of CrBr₃, where strain generates a spatial modulation of the interlayer exchange alternating between ferromagnetic and antiferromagnetic. With S=3/2 moments, the system admits a classical bilayer description with competing interactions. I develop a theoretical framework capturing the resulting non-collinear orders and reproducing experimental signatures, demonstrating how moiré engineering stabilizes non-trivial magnetic textures. The second project examines quantum magnetism in a WSe₂/WS₂ heterobilayer at three-quarters filling, where electrons form an effective kagome lattice. From the underlying Hubbard model, I derive a frustrated Heisenberg Hamiltonian with competing exchanges. Using Schwinger-boson mean-field theory, I map a phase diagram of non-collinear orders and spin-liquid phases. For realistic parameters, the ground state is a chiral spin liquid, highlighting transition-metal dichalcogenide moiré materials as platforms for topological and strongly correlated magnetism. The third project investigates quantum phase-transition dynamics with superconducting circuit quantum simulators, focusing on Hamiltonian ramps in the 2D XY model. An analogue-digital protocol drives the system from a gapped staggered state to the gapless XY phase. Analysis of correlations reveals scaling of the correlation length with ramp rate, broadly consistent with Kibble–Zurek predictions, with deviations reflecting finite-size, dimensionality, and experimental constraints. The fourth project develops a Holstein–Primakoff spin-wave description for the same XY ramps. Adapting the quantization axis to the instantaneous magnetization, this solvable quadratic theory provides magnon dispersions, time- and space-dependent correlations, and single-magnon dynamics, including decay and scattering. This framework offers a detailed picture of non-equilibrium quasiparticle behavior in a 2D magnet under time-dependent fields. Together, these projects show how moiré materials and quantum simulators enable controlled studies of frustrated and strongly correlated magnetism in two dimensions. By combining analytical modeling with experimentally relevant conditions, this thesis advances understanding of how frustration, topology, and non-equilibrium dynamics shape quantum magnetic phenomena in low-dimensional systems.
We determine the ground states and excitation spectra of the paradigmatic four-flavor Heisenberg model with nearest- and next-nearest-neighbor exchange couplings on the triangular lattice in a field controlling the population imbalance of flavor pairs. Such a system arises in the strongly correlated limit of moiré bilayers of transition metal dichalcogenides in an electric displacement field or in-plane magnetic field, and can be simulated via ultracold alkaline-earth atoms. We argue that the field tunes between effective SU(4) and SU(2) symmetries in the balanced and fully polarized limits and employ a combination of mean-field calculations, flavor-wave theory, and exact diagonalization to analyze the intermediate, imbalanced regime. We find different symmetry-broken phases with simultaneous spin and excitonic order depending on the field and next-nearest-neighbor coupling. Furthermore, we demonstrate that there is a strongly fluctuating regime without long-range order that connects candidate spin liquids of the SU(2) and SU(4) limit. The strong fluctuations are facilitated by an extensive classical degeneracy of the model, and we argue that they are also responsible for a strong polarizability at 1/3 polarization that survives from the mean-field level to the exact spectrum. Published by the American Physical Society 2024