Cite as: doi:10.26081/K6RK6T

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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 the
broader phase diagram. In systems with both spin and orbital (or valley) degrees
of freedom, SU(4)-symmetric models can serve as such a starting point. In this
talk I will discuss SU(4) quantum antiferromagnets on the triangular lattice,
that arise from Mott-insulating phases of fermions with four flavors. I will
consider different fillings of the SU(4) fermions, which lead to different
representations of SU(4) on each site. First, I will discuss the case of two
fermions per site (i.e. half-filling), which corresponds to the 6-dimensional
representation of SU(4). I will argue that in this case, the low energy
properties of the model can be captured by an effective dimer model. I will then
present exact diagonalization studies of the dimer model indicating that the
ground state breaks translation invariance, forming a valence bond solid (VBS)
with a 12-site unit cell. In the second part of my talk, I will turn to the case
of a single fermion per site, corresponding to the fundamental representation of
SU(4). Based on numerical simulations using the density matrix renormalization
group (DMRG) method, supported by field-theoretical arguments, I will provide
evidence for a gapless liquid with an emergent Fermi surface in the ground state
of the system.
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