Pith. sign in

REVIEW 3 major objections 4 minor 44 references

Quantum Mott semimetal in a one-dimensional Hubbard model

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A one-dimensional spinful Hubbard model with one orbital per unit cell has a quantum Mott semimetal as its ground state — gapless spinful Dirac fermions at k=0 coexisting with a neutral spin mode, protected by inversion and particle-hole sy

desk verdict Solid ED/DMRG evidence for a c≈3 gapless phase at the flat-band particle-hole-symmetric point, but the 'phase' label needs a stability check away from t=0. read the letter →

arxiv 2607.19465 v2 pith:5YZMT54B submitted 2026-07-21 cond-mat.str-el

Boran Zhou , Taige Wang , Ya-Hui Zhang This is my paper
classification cond-mat.str-el
keywords quantumMottsemimetalone-dimensionalHubbardmodelflat-bandprojectionparticle-holesymmetryinversionC1S2phaseancillawavefunctionmany-bodypolarization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a quantum Mott semimetal — a zero-temperature phase combining itinerant gapless electrons with local moments — can occur in a one-band Hubbard model in one dimension, with no multi-orbital structure or topological Wannier obstruction. Starting from a two-orbital ladder and projecting the Hubbard repulsion onto a flat active band, the authors find that Hubbard U alone gives a ferromagnet, but adding an inter-site antiferromagnetic exchange melts it into a spin-singlet ground state. At the flat-band, particle-hole-symmetric point, this ground state is a C1S2 phase with central charge c≈3: a spinful Dirac fermion at k=0 formed by an emergent composite fermion together with a gapless neutral spin mode from local moments. If correct, this is the first unbiased numerical evidence for such a quantum Mott semimetal, and it shows that the essential ingredients are a momentum-dependent form factor plus inversion and particle-hole symmetry. Breaking particle-hole symmetry by adding dispersion converts the semimetal into a Mott insulator with polarization 1/2, distinct from the conventional Mott insulator, with a continuous transition between the two at a Luttinger-liquid critical point.

What carries the argument

The central object is the projected f-orbital operator on the active flat band, whose momentum-space form factor g_{k_*}(k) is controlled by a single scale k_*; this nonlocal operator encodes the orbital character and sets the interaction range to 1/k_*. The argument is carried by the emergent composite fermion ψ at k=0: because inversion acts as c_{k}→c_{-k} and ψ_{k}→−ψ_{-k}, the hybridization between c and ψ must vanish linearly at k=0 (giving kσ_y), while particle-hole symmetry forbids the mass term mτ_z, so the Dirac point is protected. The ancilla wavefunction — two auxiliary fermions per site projected into a spin singlet, with the ancilla on the bond and carrying inverted parity — pr

What would settle it

Start from the C1S2 ground state at t=0 and add an arbitrarily small hopping that preserves both inversion and particle-hole symmetry (for example, a next-nearest-neighbor hopping t_A≠0 with t_B adjusted so the band remains flat, or a PH-symmetric nearest-neighbor interaction), then measure the single-electron gap in iDMRG as a function of the perturbation strength. If the gap opens linearly for any nonzero perturbation, the phase exists only at a measure-zero point and is not a symmetry-protected phase.

Watch

Extended reading notes

Core claim

The paper claims that the ground state of the projected one-orbital Hubbard model, at t=0 (flat band, particle-hole symmetric) and with antiferromagnetic exchange J_A above a critical value, is a gapless C1S2 Mott semimetal. The state contains a spinful Dirac crossing at k=0 for each spin, protected by inversion symmetry (which forces the emergent fermion ψ to have opposite parity to the electron c, making the hybridization linear in k) and by particle-hole symmetry (which forbids the Dirac mass term mτ_z). Coexisting with this itinerant sector is a gapless neutral spin mode from the local moments, giving central charge c≈3. The authors support this with exact diagonalization and density-mat

Load-bearing premise

The quantum Mott semimetal is established at the exactly flat, particle-hole-symmetric point t=0, and the paper itself notes that the model with only U_A and J_A is fine-tuned; if infinitesimal symmetry-preserving perturbations of the Hamiltonian generically open a gap or destabilize the C1S2 state, the central claim that the model hosts a protected quantum Mott semimetal phase fails.

Editorial extensions

If this is right

  • If the C1S2 Mott semimetal is genuine, Mott semimetal physics does not require topological bands, concentrated Berry curvature, or a Wannier obstruction — a momentum-dependent form factor plus inversion and particle-hole symmetries suffice.
  • The phase is a 1D laboratory for fractionalized Fermi liquid (FL*) physics emerging from a single electronic band: a composite fermion ψ that carries the electron's charge but opposite parity, hybridizing with the bare electron to form a protected Dirac node.
  • The P=1/2 Mott insulator and its continuous transition to the P=0 Mott insulator at a Luttinger-liquid critical point provide a concrete route to a many-body polarization jump of 1/2, with boundary Friedel oscillations as a signature.
  • The ancilla wavefunction and the identification of ψ as a density trion or spin polaron predict specific composite spectral features (missing spectral weight near k=0 in the upper Hubbard band) that can be probed in photoemission-like measurements or cold-atom quantum simulations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The C1S2 phase is demonstrated only at the exactly flat, particle-hole-symmetric point, and the paper itself states that the model is fine-tuned in that the k=0 mode decouples; a natural next step, not performed here, is a systematic study of infinitesimal symmetry-preserving perturbations to see whether a gap opens and whether the phase has a finite basin of attraction.
  • Because the Dirac point sits at a single momentum k=0 in one dimension, the 'semimetal' is a zero-dimensional node; comparing the numerically extracted exponents (e.g., spin correlation decay r^{-α} and pairing exponent α=1+1/K_c) against the bosonized C1S2 theory would test whether the phase is indeed the claimed SU(2)_1 × C1S1 theory or a different gapless state.
  • The claim that this 1D model 'captures essential aspects of TBG physics' suggests a testable extension: tuning the form factor g_{k_*} in the same chain interpolates between flat-band-like and topologically nontrivial limits, which could clarify which features of twisted bilayer graphene are generic to strong correlations rather than specific to its band geometry.
  • If the ancilla framework is correct, the emergent ψ fermion should leave fingerprints in bipartite entanglement spectra — a chiral two-band structure with the same central charge c≈3 — which can be computed from the variational wavefunction and checked against iDMRG.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper studies a 1D spinful Hubbard model obtained by projecting a two-orbital model onto a flat band. At the flat-band, particle-hole-symmetric point t=0, and with antiferromagnetic exchange J_A above a critical value, it claims a quantum Mott semimetal* ground state (C1S2) with central charge c≈3, consisting of a spinful Dirac fermion at k=0 and a gapless neutral spin mode. Evidence is from ED Hubbard bands touching at k=0, iDMRG finite-entanglement scaling c≈3, power-law spin correlations, and extrapolated zero single-electron and pair gaps. For t≠0 (PH breaking), the paper finds two Mott insulators distinguished by many-body polarization P=1/2 and P=0, with a continuous transition through a Luttinger liquid. An ancilla wavefunction with two auxiliary fermions is proposed and shown to have high per-site overlap with DMRG for the P=1/2 insulator.

Significance. If the central claim holds, this is the first unbiased numerical demonstration of a zero-temperature quantum Mott semimetal in a one-orbital 1D model, going beyond thermal Mott semimetals and providing a concrete toy model for the heavy-fermion/composite-fermion picture proposed for TBG. The strength of the paper is the combination of ED and iDMRG with explicit analytic spin-wave, bosonization, and RG analyses; the ancilla wavefunction achieves ~0.995 per-site overlap with DMRG, which is a nontrivial variational achievement. The C1S2 assignment from c≈3 and gapless spin/pair/electron channels is internally consistent. However, the significance of the result as a robust phase, rather than a fine-tuned critical point, is not fully established.

major comments (3)
  1. [§Quantum Mott semimetal* phase and Appendix D] The k*=0.5 point is one of the two representative C1S2 examples, with U=0 (main text: 'two example points ... J_A=4/3, U=1/15, k*=∞ and J_A=0.5, U=0, k*=0.5'). Since g_{k*}(0)=0 in Eq. (3), the k=0 electron does not enter U_A or J_A. Appendix D admits that 'the model with only the U_A and J_A term is fine tuned in the sense that the k=0 mode simply decouples.' At U=0, the k=0 c-mode is therefore completely noninteracting and dispersionless. The measured c≈3 in Fig. 2(c) for k*=0.5 may then be the trivial sum of a free spinful flat-band mode (c=2) and a Heisenberg spin chain (c=1), rather than a genuine Mott semimetal with an emergent hybridized fermion. Please provide a k*=0.5 (or similar) example with U>0, or demonstrate explicitly that the k=0 mode acquires a finite velocity and finite overlap with the composite ψ operators despite the vanishing of g_{k*}(0).
  2. [Abstract and §Symmetric Mott insulators / Appendix G] The load-bearing assertion is that the C1S2 state is a 'phase' protected by inversion and particle-hole symmetry. The microscopic model has t=0 exactly; Fig. 3(d) shows that t=0.08 gaps the Dirac point, and t is the only single-particle kinetic term. Thus C1S2 occupies a measure-zero set in the bare parameter space unless it is stable to all PH-preserving perturbations. The RG analysis in Appendix G (Eqs. G16-G34) is performed for the ancilla effective theory, not for the microscopic Hamiltonian Eq. (2), and no connection is made between the microscopic couplings (U_A, J_A, U, J) and the effective couplings (K_c, g_{J,⊥}, g_N) needed for stability. The sentence in the main text that C1S2 'appears to be stable within the numerical precision we can reach for the parameter studied' does not address PH-preserving perturbations outside the studied line. To support the 'phase' claim, please ad
  3. [End Matter, Eq. (11)] The microscopic identification of the emergent ψ fermion is left incomplete. The density trion and spin polaron operators in Eq. (11) contain the combination (c_i - c_{i+1}), whose Fourier transform is ∝ sin(k/2); the same is true of [f_{A,i+1/2}, H_int] used in Eq. (10). At the Dirac point k=0 these explicit operators have vanishing single-particle overlap. The paper states that A_0=0 but does not give a concrete microscopic operator with nonzero ψ_0 overlap. If the composite ψ_0 has zero weight in all low-energy operators, the two-band effective description (Eq. (8)) is not microscopically justified. Please compute the overlap of the candidate ψ operators with the actual low-energy excitations (e.g., via DMRG/ED spectral weights) or provide the missing k=0 construction.
minor comments (4)
  1. [General] Typos: 'demosntrated' in Conclusion, 'descandants' in the ancilla section, 'Diffrent' in Appendix C, 'Definiton' in Appendix D, 'sturcture factor' in Appendix G.
  2. [Ancilla wavefunction section] The benchmark of the ancilla wavefunction is referred to in the text as 'Fig. 3(d)', but the actual overlap/energy panel is Fig. 4(c); Fig. 3(d) is the spectral function for t=0.08. Please correct the cross-reference.
  3. [Eq. (2) and Fig. 2] It would be helpful to state explicitly in the C1S2 section which couplings (U, J) are non-zero in the two example points; the main text gives U=1/15, J=0 for k*=∞ and U=0, J=0 for k*=0.5, but the figure caption for Fig. 2(c) lists U=1/15 without distinguishing the two cases. A table of parameters would remove ambiguity.
  4. [Fig. 2(c)] The central charge extraction uses 'the last-four-point fit' of S vs ln ξ. Please provide the fitting window, the number of points, and an estimate of the statistical/finite-χ error, as the c≈3 value is a cornerstone of the C1S2 assignment.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the C1S2 identification rests on direct ED/DMRG evidence, and the ancilla/ψ effective theory is an interpretive model introduced after the numerics.

full rationale

The paper's central claim—a C1S2 quantum Mott semimetal ground state at the flat-band, particle-hole-symmetric point—is supported by direct numerical evidence rather than by an assumed input: finite-entanglement scaling gives c≈3 (Fig. 2c), single-electron and pair gaps extrapolate to zero (Fig. 8a,b), the spin correlator decays as r^{-1} (Fig. 2c), and ED shows Hubbard bands touching at k=0 (Fig. 2b). These observations do not presuppose the ancilla or ψ effective theory. The emergent fermion ψ and the low-energy Hamiltonian H_charge are introduced after the numerics as an interpretation of the observed two-component Dirac structure; they are not used to derive the ground-state phase. The single variational parameter Φ_b in the ancilla wavefunction is fitted to maximize overlap with DMRG, but this is presented as an accurate variational description, not as a prediction of the phase. Prior self-citations ([22], [37]) provide a framework and analogy, but the present numerical phase identification is independent of them, and no uniqueness theorem is invoked. The fine-tuning/robustness question at t=0 is a physical correctness concern, not a circularity issue. Overall, the derivation chain is self-contained with respect to its numerical benchmarks.

Assumptions & free parameters 4 free parameters · 5 assumptions · 2 invented entities

The ledger is moderately loaded. The model inputs k_* and J_A are physical couplings, but k_* is explored at two hand-picked values and J_A is tuned above the critical melting field; in that sense the central phase is not a parameter-free prediction. The ancilla framework adds two auxiliary fermions (ψ, ψ') and a fitted hybridization Φ_b. The projection onto the flat band and the fine-tuned t=0 point are domain assumptions. No invented entities are given independent falsifiable handles outside the paper's own numerics.

free parameters (4)
  • k_* = ∞ (large-k* limit) and 0.5
    This momentum scale enters g_{k_*}(k) and sets the interaction range 1/k_*; the authors state the model is fully decided by this function. It is a hand-chosen Hamiltonian parameter (γ/t_B), not fitted to data, but the central phase is demonstrated only at these two values.
  • J_A = 4/3 (k*=∞) and 0.5 (k*=0.5)
    Chosen above the critical J_A,c to stabilize the spin-singlet C1S2 phase; the phase does not exist at J_A=0, where the ground state is ferromagnetic. This is an input coupling, not a fit, but it is load-bearing.
  • Φ_b (ancilla variational parameter) = 0.4 (optimal)
    Variational hybridization in the ancilla Hamiltonian Eq. (6); selected by maximizing overlap with DMRG (Fig. 4). Used to validate the ancilla description, not to define the phase.
  • µ_ψ (ancilla chemical potential) = chosen so ⟨n_ψ⟩=1 per site
    Chemical potential in the ancilla Hamiltonian constrains ψ occupancy; an auxiliary construction parameter rather than a fit to external data.
assumptions (5)
  • domain assumption The two-orbital Hamiltonian can be projected onto the perfectly flat lower band because U_A is much smaller than the band gap.
    Model section: 'We assume that the Hubbard U_A is much smaller than that of the band gap and then we just project the interaction to the flat band.' The effective one-orbital model Eq. (2) depends on this projection.
  • domain assumption At t_A=0 and Δ=γ²/(2t_B)-t_B the lower band is exactly flat, giving t=0 in the effective model and exact particle-hole symmetry.
    Model section; the Mott semimetal* is analyzed at this fine-tuned point.
  • standard math Inversion, particle-hole, and time-reversal act on c and ψ as specified, forcing the k τ_y hybridization and forbidding mτ_z and k τ_x.
    Low-energy effective theory Eq. (8) and symmetry discussion; standard symmetry analysis of a two-band Dirac Hamiltonian.
  • ad hoc to paper The low-energy Hilbert space can be represented by physical electrons c, ancilla fermion ψ, and spinon ψ' with a local singlet projection.
    Eq. (5) ancilla wavefunction; a variational postulate, supported only by its benchmark against DMRG.
  • domain assumption The gapless spin sector is described by the SU(2)_1 CFT (1D Heisenberg chain).
    Ancilla framework and bosonization in Appendix G; consistent with observed power-law spin correlations but not derived from the microscopic Hamiltonian.
invented entities (2)
  • ψ ancilla fermion (composite fermion)
    purpose: Forms the second component of the Dirac fermion at k=0 and hybridizes with c in the effective two-band charge theory.
    Postulated in the ancilla wavefunction and effective theory (Eqs. 5-8). A microscopic composite form (density trion/spin polaron) is proposed in the End Matter and its spectral function matches ED, but this is internal consistency, not an independent falsifiable prediction.
  • ψ' ancilla fermion (spinon)
    purpose: Carries the neutral gapless spin mode and is singlet-projected with ψ.
    The power-law spin correlator is independent numerical evidence for a gapless spin sector, but the specific ψ' mapping and SU(2)_1 structure are interpretive.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum Mott semimetal in a one-dimensional Hubbard model." pith.science (2026). https://pith.science/paper/5YZMT54B

@misc{pith2026260719465,
  author       = {Pith},
  title        = {Pith review of: Quantum Mott semimetal in a one-dimensional Hubbard model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5YZMT54B}},
  note         = {Machine review of arXiv:2607.19465}
}
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.

Figures

Figures reproduced from arXiv: 2607.19465 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic illustration of the one-dimensional two [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Phase diagram as a function of [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. (a)(b) The illustration of the ancilla wavefunctions. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Wannier representation of the lower band. We choose [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) We calculate the effective model at [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: In the calculation we use gaussian function √ 1 2πσ e − x 2 2σ2 with σ = 0.01 to approximate δ(x). 2. Analytical calculation of spectral function Here we provide the analytical derivation of the single-particle spectral function discussed in the main text. At t = 0, th…
Figure 8
Figure 8. Figure 8: FIG. 8. Finite size and finite correlation length scaling in the Mott semimetal [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. MPS representation for the ancilla wavefunction. (a)(b) MPS representation for (a) [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Bond-singlet pairing of the [PITH_FULL_IMAGE:figures/full_fig_p022_10.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

44 extracted references · 4 linked inside Pith

  1. [1]

    E. Y. Andrei, D. K. Efetov, P. Jarillo-Herrero, A. H. MacDonald, K. F. Mak, T. Senthil, E. Tutuc, A. Yazdani, and A. F. Young, The marvels of moir´ e materials, Nat. Rev. Mater.6, 201 (2021)

    2021

  2. [2]

    K. F. Mak and J. Shan, Semiconductor moir´ e materials, Nat. Nanotechnol.17, 686 (2022)

    2022

  3. [3]

    Balents, C

    L. Balents, C. R. Dean, D. K. Efetov, and A. F. Young, Superconductivity and strong correlations in moir´ e flat bands, Nat. Phys.16, 725 (2020)

    2020

  4. [4]

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, 6 J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo- Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature556, 80 (2018)

    2018

  5. [5]

    Rozen, J

    A. Rozen, J. M. Park, U. Zondiner, Y. Cao,et al., En- tropic evidence for a Pomeranchuk effect in magic-angle graphene, Nature592, 214 (2021)

    2021

  6. [6]

    Saito, F

    Y. Saito, F. Yang, J. Ge, X. Liu,et al., Isospin Pomer- anchuk effect in twisted bilayer graphene, Nature592, 220 (2021)

    2021

  7. [7]

    D. Wong, K. P. Nuckolls, M. Oh, B. Lian, Y. Xie, S. Jeon, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yaz- dani, Cascade of electronic transitions in magic-angle twisted bilayer graphene, Nature582, 198 (2020)

    2020

  8. [8]

    Zondiner, A

    U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, A. Stern, E. Berg, P. Jarillo-Herrero, and S. Ilani, Cascade of phase transitions and dirac revivals in magic- angle graphene, Nature582, 203 (2020)

    2020

Show all 44 references
  1. [9]

    A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney,et al., Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science365, 605 (2019)

    2019

  2. [10]

    Serlin, C

    M. Serlin, C. L. Tschirhart, H. Polshyn,et al., Intrinsic quantized anomalous Hall effect in a moir´ e heterostruc- ture, Science367, 900 (2020)

    2020

  3. [11]

    Bultinck, E

    N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vish- wanath, and M. P. Zaletel, Ground state and hidden symmetry of magic-angle graphene at even integer fill- ing, Phys. Rev. X10, 031034 (2020)

    2020

  4. [12]

    Y. H. Kwan, G. Wagner, T. Soejima, M. P. Zaletel, S. H. Simon, S. A. Parameswaran, and N. Bultinck, Kekul´ e spi- ral order at all nonzero integer fillings in twisted bilayer graphene, Phys. Rev. X11, 041063 (2021)

    2021

  5. [13]

    D. E. Parker, T. Soejima, J. Hauschild, M. P. Zaletel, and N. Bultinck, Strain-induced quantum phase transitions in magic-angle graphene, Phys. Rev. Lett.127, 027601 (2021)

    2021

  6. [14]

    Wagner, Y

    G. Wagner, Y. H. Kwan, N. Bultinck, S. H. Simon, and S. A. Parameswaran, Global phase diagram of the normal state of twisted bilayer graphene, Phys. Rev. Lett.128, 156401 (2022)

    2022

  7. [15]

    Bultinck, S

    N. Bultinck, S. Chatterjee, and M. P. Zaletel, Mecha- nism for anomalous hall ferromagnetism in twisted bi- layer graphene, Phys. Rev. Lett.124, 166601 (2020)

    2020

  8. [16]

    Zhang, D

    Y.-H. Zhang, D. Mao, and T. Senthil, Twisted bilayer graphene aligned with hexagonal boron nitride: Anoma- lous hall effect and a lattice model, Phys. Rev. Res.1, 033126 (2019)

    2019

  9. [17]

    Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo- Herrero, and A. Yacoby, Fractional chern insulators in magic-angle twisted bilayer graphene, Nature600, 439 (2021)

    2021

  10. [18]

    Zhang, D

    Y.-H. Zhang, D. Mao, Y. Cao, P. Jarillo-Herrero, and T. Senthil, Nearly flat Chern bands in moir´ e superlat- tices, Phys. Rev. B99, 075127 (2019)

    2019

  11. [19]

    Repellin, Z

    C. Repellin, Z. Dong, Y.-H. Zhang, and T. Senthil, Ferro- magnetism in narrow bands of moir´ e superlattices, Phys. Rev. Lett.124, 187601 (2020)

    2020

  12. [20]

    P. J. Ledwith, J. Dong, A. Vishwanath, and E. Kha- laf, Nonlocal moments and mott semimetal in the chern bands of twisted bilayer graphene, Phys. Rev. X15, 021087 (2025)

    2025

  13. [21]

    Hu, Z.-D

    H. Hu, Z.-D. Song, and B. A. Bernevig, Projected and solvable topological heavy fermion model of twisted bi- layer graphene (2025), arXiv:2502.14039 [cond-mat.str- el]

    2025

  14. [22]

    J.-Y. Zhao, B. Zhou, and Y.-H. Zhang, Topological Mott localization and pseudogap metal in twisted bilayer graphene, Phys. Rev. B112, 085107 (2025)

    2025

  15. [23]

    P. J. Ledwith, A. Vishwanath, and E. Khalaf, Exotic car- riers from concentrated topology: Dirac trions as the origin of the missing spectral weight in twisted bilayer graphene, arXiv preprint arXiv:2505.08779 (2025)

    2025 arXiv

  16. [24]

    J.-Y. Zhao, B. Zhou, and Y.-H. Zhang, Mixed-valence mott insulator and composite excitation in twisted bi- layer graphene, Phys. Rev. B112, 235144 (2025)

    2025

  17. [25]

    Vituri and E

    Y. Vituri and E. Berg, Controlled loop expan- sion for the topological heavy fermion model (2026), arXiv:2604.14278 [cond-mat.str-el]

    2026 arXiv

  18. [26]

    N. Wei, F. von Oppen, and L. I. Glazman, Lifetime and spectral function of topological heavy fermions (2026), arXiv:2604.14369 [cond-mat.str-el]

    2026 arXiv

  19. [27]

    P. A. Nosov, E. Khalaf, and P. Ledwith, Controlled ex- pansion for correlated electrons with concentrated kine- matics (2026), arXiv:2605.20171 [cond-mat.str-el]

    2026 arXiv

  20. [28]

    Zhou and Y.-H

    B. Zhou and Y.-H. Zhang, Symmetric topological mott insulator and mott semimetal, arXiv preprint arXiv:2601.02485 (2026)

    2026

  21. [29]

    W.-P. Su, J. Schrieffer, and A. Heeger, Soliton excitations in polyacetylene, Physical Review B22, 2099 (1980)

  22. [30]

    Senthil, S

    T. Senthil, S. Sachdev, and M. Vojta, Fractionalized fermi liquids, Phys. Rev. Lett.90, 216403 (2003)

    2003

  23. [31]

    Rende, A

    R. Rende, A. Nikolaenko, L. L. Viteritti, S. Sachdev, and Y.-H. Zhang, Transformer neural-network quan- tum states for lattice models of spins and fermions: Application to the ancilla layer model, arXiv preprint arXiv:2603.02316 (2026)

    2026

  24. [32]

    Resta, Quantum-mechanical position operator in ex- tended systems, Phys

    R. Resta, Quantum-mechanical position operator in ex- tended systems, Phys. Rev. Lett.80, 1800 (1998)

    1998

  25. [33]

    Tada and M

    Y. Tada and M. Oshikawa, Many-body multipole index and bulk-boundary correspondence, Phys. Rev. B108, 235150 (2023)

    2023

  26. [34]

    E. G. Dalla Torre, E. Berg, and E. Altman, Hidden order in 1d bose insulators, Phys. Rev. Lett.97, 260401 (2006)

    2006

  27. [35]

    Barbiero, A

    L. Barbiero, A. Montorsi, and M. Roncaglia, How hid- den orders generate gaps in one-dimensional fermionic systems, Phys. Rev. B88, 035109 (2013)

    2013

  28. [36]

    Montorsi, F

    A. Montorsi, F. Dolcini, R. C. Iotti, and F. Rossi, Symmetry-protected topological phases of one- dimensional interacting fermions with spin-charge separation, Phys. Rev. B95, 245108 (2017)

    2017

  29. [37]

    Zhou, H.-K

    B. Zhou, H.-K. Jin, and Y.-H. Zhang, Variational wave- function for a mott insulator at finiteuusing ancilla qubits, Phys. Rev. B112, 115159 (2025)

    2025

  30. [38]

    Zhang and S

    Y.-H. Zhang and S. Sachdev, From the pseudogap metal to the Fermi liquid using ancilla qubits, Phys. Rev. Res. 2, 023172 (2020)

    2020

  31. [39]

    Hubbard, Electron correlations in narrow energy bands, Proceedings of the Royal Society of London

    J. Hubbard, Electron correlations in narrow energy bands, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences276, 238 (1963). End Matter 7 (𝑏) (𝑐) (𝑑)(𝑎) FIG. 5. Wannier representation of the lower band. We chooset A = 0, tB =−1, γ= 1 in the calcu...

    1963

  32. [40]

    The spectral function for is shown in Fig

    Definiton of spectral function Here we provide the details of calculating the spectral functionA(k, ω), which is defined as: A(k, ω) = X σ 1 Z X ⟨m|∈Ne+1 X |n⟩∈Ne e− En T ⟨m|c† k;σ|n⟩δ(ω−(E m −E n)) + 1 Z X ⟨m|∈Ne−1 X |n⟩∈Ne e− En T ⟨m|c−k;¯σ|n⟩δ(ω−(E n −E m)) ! , (D2) whereZi...

  33. [41]

    Analytical calculation of spectral function Here we provide the analytical derivation of the single-particle spectral function discussed in the main text. At t= 0, the projected effective Hamiltonian can be written as Heff = X i UA 2 ˜nA;i+ 1 2 −1 2 + U 2 (ni −1) 2 + X i JA 2 ...

  34. [42]

    (G4) The shifts are defined modulo the compactification periods

    Symmetries and allowed perturbations The symmetry transformations of the fields are: I:ϕ c(x)→ −ϕc(−x) + π 2 , θ c(x)→θ c,s(−x), ϕs → −ϕs(−x), θ s(x)→θ s(−x), C:ϕ c,s(x)→ −ϕc,s(x), θ c,s(x)→θ c,s(x), T:ϕ c(x)→ϕ c(x), θ c(x)→ −θc(x)− π 2 , ϕs(x)→ −ϕs(x), θ s(x)→θ s(x) + π 2 . (...

  35. [43]

    Momentum-shell integration After integrating outθ ν and settingy ν =v ντwherev ν is charge/spin velocity. The Euclidean action is S= X ν 1 2πKν Z d2r(∇ϕ ν)2.(G8) Splitϕ ν =ϕ ν,< +ϕ ν,> with ϕ< :|q|<Λe −dℓ, ϕ > : Λe−dℓ <|q|<Λ,Λ =α −1.(G9) The fast-mode fluctuations can be calcu...

  36. [44]

    Coupling to the neutral spin mode If we consider the coupling to the neutral spin modeψ ′, the most general coupling is HJ =J cSc ·S ψ′ +J ψSψ ·S ψ′.(G18) We bosonize the spin field ofψ ′, the details are given in Table. III. Terms containing (−1) iN ′ oscillate and average to...

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.