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Dimer description of the SU(4) antiferromagnet on the triangular lattice

by Anna Keselman, Lucile Savary, Leon Balents

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Submission summary

Authors (as registered SciPost users): Anna Keselman
Submission information
Preprint Link:  (pdf)
Date accepted: 2020-04-21
Date submitted: 2020-04-10 02:00
Submitted by: Keselman, Anna
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


In systems with many local degrees of freedom, high-symmetry 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 half-filling, i.e. the six-dimensional 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 non-magnetic. 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 12-site 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.

Author comments upon resubmission

We thank the referees for the careful reading of our paper and for their comments and suggestions.
We are providing a revised version of the manuscript addressing all the questions and comments raised.

List of changes

1. In Eq. (2), and throughout the manuscript, we now use numbers 1..4 in sanf-serif font to denote the SU(4) basis states, as opposed to the standard font used to denote the SO(6) basis states.

2. We have added a reference to Phys. Rev. B 80, 064413 addressing the mapping between the SU(4) and SO(6) groups in the beginning of Sec. 2.2.

3. When discussing the flavor gap in Sec. 3.3.1, we now state that the (t3,t8,t15) = (2,0,0) sector corresponds to the 15-dimensional irreducible representation, as can be verified by calculating the value of the SU(4) quadratic Casimir operator.

4. We have added the system size and the method used to obtain Fig. 3 in its caption.

5. We have modified Fig. 3(b,d) to show the hexagonal Brillouin zone.

6. We have added a discussion regarding the breaking of the 6-fold rotational symmetry down to a 2-fold one, observed in Fig. 3(d) in Sec. 4.4.2. This symmetry breaking occurs because we peak only bonds with a specific orientation when calculating the bond-bond correlations.

7. In the effective dimer model in Eq. (37) we now label all the coefficients and list the corresponding expressions in terms of the parameters (x,\alpha, \beta), as well as their numerical values obtained for the SU(4) Heisenberg model (x=1/6,\alpha=-1,\beta=1) in Table 2. We hope this also make it easier to see which terms appear at which order in the expansion in x. In addition, when referring to H_0, H_1 and H_2 in Sec. 4.4.2, we define them explicitly in terms of these coefficients and their numerical values.

8. We have modified the caption of Fig. 4 to state that it was obtained using DMRG and is consistent with an exponential decay of the correlation function for J_H=0.

9. We have added Appendices (A.2) and (A.3) discussing the classical variational wavefunction in terms of the SU(4) basis states and relating the SU(4) formulation to the SO(6) formulation presented in (A.1).

10. We have fixed the critical value for v/t mentioned in Sec. 4.4 to be 0.83 as pointed out by the referee, and have added references to PRB 74, 134301 and PRB 76, 140404 where this value is obtained.

Published as SciPost Phys. 8, 076 (2020)

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