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Abstract Motivated by recent experimental work on moiré systems in a strong magnetic field, we compute the compressibility as well as the spin correlations and Hofstadter spectrum of spinful electrons on a honeycomb lattice with Hubbard interactions using the determinantal quantum Monte Carlo method. While the interactions in general preserve quantum and anomalous Hall states, emergent features arise corresponding to an antiferromagnetic insulator at half-filling and other incompressible states following the Chern sequence ± (2 N + 1). These odd integer Chern states exhibit strong ferromagnetic correlations and arise spontaneously without any external mechanism for breaking the spin-rotation symmetry. Analogs of these magnetic states should be observable in general interacting quantum Hall systems. In addition, the interacting Hofstadter spectrum is qualitatively similar to the experimental data at intermediate values of the on-site interaction.
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DMRG study of strongly interacting $\mathbb{Z}_2$ flatbands: a toy model inspired by twisted bilayer graphene
Strong interactions between electrons occupying bands of opposite (orlike) topological quantum numbers (Chern =\pm1 = ± 1 ),and with flat dispersion, are studied by using lowest Landau level (LLL)wavefunctions. More precisely, we determine the ground states for twoscenarios at half-filling: (i) LLL’s with opposite sign of magneticfield, and therefore opposite Chern number; and (ii) LLL’s with the samemagnetic field. In the first scenario – which we argue to be a toy modelinspired by the chirally symmetric continuum model for twisted bilayergraphene – the opposite Chern LLL’s are Kramer pairs, and thus thereexists time-reversal symmetry ( \mathbb{Z}_2 ℤ 2 ).Turning on repulsive interactions drives the system to spontaneouslybreak time-reversal symmetry – a quantum anomalous Hall state describedby one particle per LLL orbital, either all positive Chern |{++\cdots+}\rangle | + + ⋯ + ⟩ or all negative |{--\cdots-}\rangle | − − ⋯ − ⟩ .If instead, interactions are taken between electrons of like-Chernnumber, the ground state is an SU(2) S U ( 2 ) ferromagnet, with total spin pointing along an arbitrary direction, aswith the \nu=1 ν = 1 spin- \frac{1}{2} 1 2 quantum Hall ferromagnet. The ground states and some of theirexcitations for both of these scenarios are argued analytically, andfurther complimented by density matrix renormalization group (DMRG) andexact diagonalization.
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- Award ID(s):
- 1916958
- PAR ID:
- 10207501
- Date Published:
- Journal Name:
- SciPost Physics Core
- Volume:
- 3
- Issue:
- 2
- ISSN:
- 2666-9366
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.21468/SciPostPhysCore.3.2.015
