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 halffilling: (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 timereversal symmetry ( \mathbb{Z}_2 ℤ 2 ).Turning on repulsive interactions drives the system to spontaneouslybreak timereversal 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 likeChernnumber, 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, andfurthermore »
Dimer description of the SU(4) antiferromagnet on the triangular lattice
In systems with many local degrees of freedom, highsymmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)symmetric models.Here we consider SU(4)symmetric "spin'' models, corresponding to Mott phases at halffilling, i.e. the sixdimensional representation of SU(4). This may be relevant to twisted multilayer graphene.In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is nonmagnetic.We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12site unit cell.Finally, we consider the effect of SU(4)symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.
 Award ID(s):
 1725797
 Publication Date:
 NSFPAR ID:
 10202442
 Journal Name:
 SciPost Physics
 Volume:
 8
 Issue:
 5
 ISSN:
 25424653
 Sponsoring Org:
 National Science Foundation
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