Motivated by the realization of spin-valley Hubbard model on a triangular moir\'e superlattice in ABC trilayer graphene aligned with hexagon boron nitride (hBN) and possibly also in twisted transition metal dichalcogenide homobilayers, we study possible Mott insulating phases and pseudogap metals based on symmetry constraint and parton mean field theories. First, we show that the Luttinger constraint allows two distinct symmetric and featureless Fermi liquids when there is an intervalley Hund's term breaking
SU(4) spin rotation. Especially, there exists a symmetric and featureless ``pseudogap metal'' with small Fermi surfaces. Then, we suggest to search for such an unconventional metallic state by doping the Mott insulator at ${\ensuremath{\nu}}_{T}=2$. For this purpose, we study the ${\ensuremath{\nu}}_{T}=2$ Mott insulator using the
SO(6) Schwinger boson or Schwinger fermion parton. At the
SU(4)-symmetric point, we find two symmetric
Z2 spin liquids. With a large anti-intervalley Hund's term, a featureless Mott insulator is natural. Next, we show that doping the featureless Mott insulator or a
Z2 spin liquid can lead to featureless or orthogonal ``pseudogap metal'' with small Fermi surfaces proportional to the doping. Besides, we also provide one scenario for the evolution from pseudogap metal to the conventional Fermi liquid through an intermediate exotic ``deconfined metal'' phase. Last, we give brief comments on the possibility of
U(1) spinon Fermi surface state or
Z4 spin liquid at ${\ensuremath{\nu}}_{T}=1$.
Abstract The observation of strongly correlated states in moiré systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g., to describe Mott insulators where the local moments are coupled spin–valley degrees of freedom. Here, we discuss a numerical renormalization group scheme to explore the formation of spin–valley ordered and unconventional spin–valley liquid states at zero temperature based on a pseudo-fermion representation. Our generalization of the conventional pseudo-fermion functional renormalization group approach for
su s u (2) spins is capable of treating diagonal and off-diagonal couplings of generic spin–valley exchange Hamiltonians in the self-conjugate representation of the
su s u (4) algebra. To achieve proper numerical efficiency, we derive a number of symmetry constraints on the flow equations that significantly limit the number of ordinary differential equations to be solved. As an example system, we investigate a diagonal SU(2)
spin spin
⊗ ⊗ U(1)
valley valley model on the triangular lattice which exhibits a rich phase diagram of spin and valley ordered phases. Graphic Abstract
Recent advances in moiré engineering motivate the study of lattice models of strongly-correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120
∘ antiferromagnetic phases. We use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.
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.
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.
Mott physics in topological bands has recently attracted considerable attention, particularly in the context of twisted bilayer graphene (TBG). However, the essential ingredients for stabilizing this physics remain unclear. Here, we demonstrate a quantum Mott semimetal phase as the ground state within a one-dimensional spinful Hubbard model featuring only one orbital per unit cell, protected by inversion and particle-hole symmetries. We start from a two-orbital model where a localized
f orbital on the A sublattice hybridizes with a delocalized
c orbital on the B sublattice. Projecting the
f-orbital Hubbard
U onto the active flat band yields a lattice model with Wannier orbitals centered on the B sublattice. Similar to TBG, a momentum-space scale
k∗ emerges, setting the interaction range in the projected model to
1/k∗. While the ground state is ferromagnetic with only the Hubbard
U, introducing an inter-site antiferromagnetic spin coupling
J stabilizes a Mott semimetal
∗ phase with a central charge
c=3. Using exact diagonalization (ED) and density matrix renormalization group (DMRG) methods, we show that this phase hosts a spinful Dirac fermion coexisting with a neutral spin mode -- analogous to the fractionalized Fermi liquid (FL
∗) phase in higher dimensions. Furthermore, breaking particle-hole (PH) symmetry via dispersion transforms the Mott semimetal into a Mott insulator, which is separated from a distinct Mott insulating phase by a continuous transition with a polarization jump of
1/2. Our work provides the first unbiased evidence of a Mott semimetal ground state and demonstrates that this 1D model captures some essential aspects of TBG physics, despite lacking a Wannier obstruction.