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Title: 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.  more » « less
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SciPost Physics Core
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National Science Foundation
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