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Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
Strongly Correlated Electrons · Submitted 23 Jun 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.
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The abstract, sentence by sentence
We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_{2}$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. | contribution 0.82 | 0.62 | 0.03 | asserted 0.87 |
| s1 | The resulting model has remarkably rich physical properties. | interpretation 0.60 | 0.21 | 0.04 | asserted 0.99 |
| s2 | In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. | result 0.99 | 0.74 | 0.08 | asserted 1.00 |
| s3 | Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. | result 0.99 | 0.74 | 0.09 | asserted 0.99 |
| s4 | At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. | result 1.00 | 0.88 | 0.15 | asserted 1.00 |
| s5 | Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_{2}$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. | result 0.70 | 0.82 | 0.20 | asserted 1.00 |
| s6 | Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. | contribution 0.50 | 0.87 | 0.30 | speculative 0.41 |
| s7 | For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations. | result 0.99 | 0.90 | 0.19 | asserted 1.00 |
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The paper
Original abstract
We consider the Kane-Mele-Hubbard model with a magnetic $\pi$ flux threading each honeycomb plaquette. The resulting model has remarkably rich physical properties. In each spin sector, the noninteracting band structure is characterized by a total Chern number $C=\pm 2$. Fine-tuning of the intrinsic spin-orbit coupling $\lambda$ leads to a quadratic band crossing point associated with a topological phase transition. At this point, quantum Monte Carlo simulations reveal a magnetically ordered phase which extends to weak coupling. Although the spinful model has two Kramers doublets at each edge and is explicitly shown to be a $Z_{2}$ trivial insulator, the helical edge states are protected at the single-particle level by translation symmetry. Drawing on the bosonized low-energy Hamiltonian, we predict a correlation-induced gap as a result of umklapp scattering for half-filled bands. For strong interactions, this prediction is confirmed by quantum Monte Carlo simulations.
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What this paper does with the arXiv papers it cites
What it cites · 6 sentences without a confident label
Uses the method or tool of 1 paper
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Using CT-INT in combination with the stochastic maximum entropy method [ref] , we calculate the spin-averaged spectral function at the edge,
Identifying the maximum entropy method as a special limit of stochastic analytic continuation · Single-particle spectral function · 1.00
Cites as background 1 paper
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The KMH model without additional $π$ fluxes is known to exhibit long-range, transverse antiferromagnetic order at large values of $U/t$ [ref] .
Rashba spin orbit coupling in the Kane-Mele-Hubbard model · Bulk correlation effects · 0.82
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