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arXiv:2607.19465

Quantum Mott semimetal in a one-dimensional Hubbard model

B Zhou, Taige Wang, Ya-Hui Zhang

Published Jul 21, 2026• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2607.19465

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Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
We investigated the honeycomb lattice using a two-orbital (α and β) Hubbard model and many-body exact calculations. The spin gap (Δ s ), charge gap (Δ c ), intrasite ( γ i i α β = ⟨ S → i α · S → i β ⟩ ), intersite ( γ i j α β = ⟨ S → i α · S → j β ⟩ ), spin–spin correlations, and orbital magnetic moments μ iα are analyzed for different band-filling ( n ), which denotes the number of electrons per site. Special attention was set in one-quarter-filled ( n = 1) and half-filled ( n = 2) bands. The results are presented by varying Coulomb repulsion ( U), Hund’s coupling ( J H ), external magnetic field ( B ), and orbital energy splitting (Δϵ). For the one-quarter-filled band, an intrasite magnetic disorder ( γ i i α β ≈ 0 ) begins to form for large values of U / t, which is interpreted as a possible signature of a resonating valence bond state. Full orbital polarization ( γ i i α β = 0.25 ) with intersite antiferromagnetic (AFM) order ( γ i j α β = − 0.25 ) was observed in the half-filled band for U / t ≫ 1, indicating that the two-orbital Hubbard model can be mapped to an AFM Heisenberg model with S = 1. The increase of J H is conductive to insulating and metallic phases for half- and one-quarter-filled bands, respectively. For a fractional n, the honeycomb lattice can exhibit spin-glass-like behavior, predominating as a disordered magnetic system characterized by random values of γ i j α β . The magnetic field induced a reduction in Δ c, which became zero at the critical external magnetic field. Twisted bilayer graphene (TBG) exhibits approximately flat electronic bands at magic angles and interesting correlated phenomena, such as unconventional superconductivity and correlated insulating states around n = 1 and n = 2, respectively. The dominance of electron–electron interactions in TBG makes the Hubbard model, in various versions (extended or multi-orbital), offer a practical, structure-scale account for investigating many-body effects in large moiré unit cells, where first-principles density-functional theory calculations are computationally challenging.
We study the single- and many-particle properties of a two-leg ladder model threaded by a flux with the legs coupled by a spatially varying term. Although a priori unrelated to twisted bilayer graphene (TBG), the model is found to have striking similarities: a quasi-flat low-energy band emerges with characteristics similar to that of magic angle TBG. We study the effect of interparticle interaction in our model using the density matrix renormalization group and find that when the band is quasi-flat, the ground state is a ferromagnetic Mott insulator. As the band becomes more dispersive, the system undergoes a ferromagnetic to antiferromagnetic transition. We discuss how our model is relevant not only to magic-angle physics in TBG, but also in the larger context of one-dimensional correlations and magnetism.
The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands.An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions.While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit.Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality.We establish the absence of a sign problem for this model in a momentumspace approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion.Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a "pseudogap" regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature.Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.
An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semimetal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to the 3D N=4 Gross-Neveu chiral XY universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.