SciPost Phys. 8, 076 (2020) ·
published 13 May 2020
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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
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.
SciPost Phys. 7, 048 (2019) ·
published 10 October 2019
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We present a simple derivation of a continuum Hamiltonian for bilayer
graphene with an arbitrary smooth lattice deformation -- technically in a
fashion parametrized by displacement fields with small gradients. We show that
this subsumes the continuum model of Bistritzer and Macdonald for twisted
bilayer graphene as well as many generalizations and extensions of it. The
derivation is carried out entirely in real space.
Jason Iaconis, Chunxiao Liu, Gábor B. Halász, Leon Balents
SciPost Phys. 4, 003 (2018) ·
published 19 January 2018
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In this paper, we explore the relationship between strong spin-orbit coupling
and spin liquid physics. We study a very general model on the triangular
lattice where spin-orbit coupling leads to the presence of highly anisotropic
interactions. We use variational Monte Carlo to study both $U(1)$ quantum spin
liquid states and ordered ones, via the Gutzwiller projected fermion
construction. We thereby obtain the ground state phase diagram in this phase
space. We furthermore consider effects beyond the Gutzwiller wavefunctions for
the spinon Fermi surface quantum spin liquid, which are of particular
importance when spin-orbit coupling is present.
