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arXiv:2606.12530

Hidden antiferromagnetism, persistent valley fluctuations, and $U(6)$ crossovers in triangular-lattice M-point moiré materials via determinantal quantum Monte Carlo

Konstantinos Vasiliou, Dumitru Călugăru, Johannes S. Hofmann, S. A. Parameswaran

Published Jun 10, 2026• 0 citations
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Abstract

A new moiré material platform was recently proposed based on twisting two-dimensional atomic monolayers whose low-energy states lie at the three M-points of the Brillouin Zone. Continuum and ab initio modeling suggest that electrons in the conduction bands of these materials realize three-valley Hubbard models with valley-selective, quasi-one-dimensional hopping. Remarkably, the onsite Hubbard repulsion is almost $U(6)$-symmetric without fine-tuning. Here, we show that this class of systems naturally admits sign-free determinantal Quantum Monte Carlo simulations at a filling of three electrons per moiré unit cell. We use these to explore the phase diagram for interactions of various strengths and $U(6)$-breaking anisotropies. We show that for near-isotropic interactions as relevant to, e.g., AA-stacked twisted SnSe$_2$, the system exhibits an extended intermediate-coupling regime in which local-moment formation and itinerancy compete, and the crossover to a putative low-temperature ordered state can be understood in terms of fluctuating $U(6)$ local moments. We argue that many of these features persist beyond the idealized sign-problem-free limit.

DOI
10.48550/arxiv.2606.12530

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Hidden antiferromagnetism, persistent valley fluctuations, and U(6)U(6)U(6) crossovers in triangular-lattice M-point moiré materials via determinantal quantum Monte Carlo
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Moir\'e systems offer an exciting playground to study the many-body effects of strongly correlated electrons in regimes that are not easily accessible in conventional material settings. Motivated by a recent experiment on WSe2/WS2{\text{WSe}}_{2}/{\text{WS}}_{2}WSe2​/WS2​ moir\'e bilayers [Y. Tang et al., Nature (London) 579, 353 (2020)], which realized a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice for intermediate temperatures $t\ensuremath{\lesssim}T<U$. Employing finite-temperature Lanczos calculations and closely following the fitting protocols used in the experiment, we recover the observed trends in the reported Curie-Weiss temperature $\mathrm{\ensuremath{\Theta}}$ with filling, using the reported interaction strength U/t=20U/t=20U/t=20. We focus on the large increase of $|\mathrm{\ensuremath{\Theta}}|$ on decreasing the density below half filling and the sign change of $\mathrm{\ensuremath{\Theta}}$ at higher fillings, which signals the onset of ferromagnetism. The increase in $|\mathrm{\ensuremath{\Theta}}|$ is also seen in the $t\ensuremath{-}J$ model (the low-energy limit of the Hubbard model) in the intermediate temperature range, which we clarify is opposite to the trend in its high temperature limit. Differences between the low, intermediate, and high temperature regimes are discussed. Our numerical calculations also capture the crossover between short-range antiferromagnetic to ferromagnetic order in the intermediate temperature regime, a result broadly consistent with the experimental findings. We find that this behavior is a finite-temperature remnant of the underlying zero-temperature phase transition, which we explore with ground-state density matrix renormalization group calculations. We provide evidence of ferromagnetism characterized by weak (but robust) correlations that explain the small $\mathrm{\ensuremath{\Theta}}$ seen in the experiment.
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An SU(4)SU(4)SU(4) chiral spin liquid and quantized dipole Hall effect in moir\'e bilayers
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A wide variety of experimental platforms, ranging from semiconductor quantum-dot arrays to moiré materials, have recently emerged as powerful quantum simulators for studying the Hubbard model and its variants. Motivated by these developments, here, we investigate a generalization of the Hubbard model which includes the effects of long-range Coulomb interactions. Working on finite-sized two-dimensional square and triangular lattices, we use exact diagonalization and density-matrix renormalization group calculations to probe the magnetic structure of the ground state in the strong-coupling regime, where UUU (the onsite repulsion) ≫\gg≫ ttt (the nearest-neighbor hopping). For small electron dopings above the half-filled antiferromagnet, we numerically uncover a rich variety of magnetically ordered states, and in conjunction with theoretical arguments, infer the phase diagram of the system as a function of doping and interaction strengths. In particular, we find that the inclusion of long-range Coulomb interactions induces an instability of high-spin states$\unicode{x2014}$such as the saturated Nagaoka ferromagnet$\unicode{x2014}$towards phase separation and stripe ordering. We also present proposals for the observation of some of our key findings in experiments that would shed further light on this paradigmatic strongly correlated system.