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arXiv:2105.07008 · Physical Review Letters

Quantum Phases of Transition Metal Dichalcogenide Moiré Systems

Yiqing Zhou, D. N. Sheng, Eun-Ah Kim

Published Apr 14, 2022• 26 citations
arXivHTMLPDF

Abstract

Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on heterobilayer transition metal dichalcogenide Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-transition metal dichalcogenide Moiré system's potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group. Specifically, we explore the two-dimensional phase space spanned by the key tuning parameters in the extended Hubbard model, namely, the kinetic energy strength and the further-range Coulomb interaction strengths. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge order. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.

DOI
10.1103/physrevlett.128.157602

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Moiré systems provide a rich platform for studies of strong correlation physics. Recent experiments on heterobilayer transition metal dichalcogenide Moiré systems are exciting in that they manifest a relatively simple model system of an extended Hubbard model on a triangular lattice. Inspired by the prospect of the hetero-transition metal dichalcogenide Moiré system's potential as a solid-state-based quantum simulator, we explore the extended Hubbard model on the triangular lattice using the density matrix renormalization group. Specifically, we explore the two-dimensional phase space spanned by the key tuning parameters in the extended Hubbard model, namely, the kinetic energy strength and the further-range Coulomb interaction strengths. We find competition between Fermi fluid, chiral spin liquid, spin density wave, and charge order. In particular, our finding of the optimal further-range interaction for the chiral correlation presents a tantalizing possibility.
At n=3/4n=3/4n=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 WSe2_22​/WS2_22​, 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.
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∘120^\circ120∘-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.
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Quantum spin liquids emerging near the metal-insulator transition have been a longstanding issue in physics. Here, the author identifies a chiral spin liquid in the half-filled triangular-lattice Hubbard model using state-of-the-art non-Abelian density matrix renormalization. By computing the spin chirality order parameter with unprecedented system sizes and high accuracy, the findings extrapolate toward the two-dimensional limit, impacting theoretical research and experimental realizations in ultracold-atom optical lattices and transition-metal dichalcogenide moir\'e materials.
In this work, we study a slave-rotor mean-field theory of an extended Hubbard model, applicable to transition metal dichalcogenide moir\'e systems, that captures both the formation of Wigner crystals as well as exotic spin states on top of these charge backgrounds. Phase diagrams are mapped out for different choices of long-range Coulomb repulsion strength, reproducing several experimentally found Wigner crystal states. Assuming unbroken time-reversal symmetry, we find several spin-liquid states as well as dimer states at fractional fillings. While spin dimer states are always found to have the lowest mean-field energy, several spin-liquid states are energetically competitive and may be stabilized by including gauge fluctuations or further interaction terms. We further discuss possible experimental signatures of these states pertinent to two-dimensional moir\'e heterostructures.
Abstract We study the ground-state properties of twisted transition metal dichalcogenide (TMD) hetero-bilayers using density matrix renormalization group (DMRG) simulations of an effective spin model with four-spin ring exchange interactions. Our results demonstrate a gapless quantum spin liquid (QSL) phase, stabilized by the ring exchange term, and a competing valence bond solid (VBS) phase. The QSL exhibits power-law spin correlations and a central charge consistent with multiple gapless modes. Tuning the dielectric constant drives a continuous transition between these phases. Our results emphasize the role of ring exchange interactions in moiré TMDs and demonstrate their potential as quantum simulators.