SciPost Phys. 8, 076 (2020) ·
published 13 May 2020

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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.
Anna Keselman, Chaitanya Murthy, Bernard van Heck, Bela Bauer
SciPost Phys. 7, 050 (2019) ·
published 16 October 2019

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We study nanowirebased Josephson junctions shunted by a capacitor and take into account the presence of lowenergy quasiparticle excitations. These are treated by extending conventional models used to describe superconducting qubits to include the coherent coupling between fermionic quasiparticles, in particular the Majorana zero modes that emerge in topological superconductors, and the plasma mode of the junction. Using accurate, unbiased matrixproduct state techniques, we compute the energy spectrum and response function of the system across the topological phase transition. Furthermore, we develop a perturbative approach, valid in the harmonic limit with small charging energy, illustrating how the presence of lowenergy quasiparticles affects the spectrum and response of the junction. Our results are of direct interest to ongoing experimental investigations of nanowirebased superconducting qubits.