Layered Kitaev-Ising spin-orbital models map to N-flavor Hubbard models with emergent SU(N) symmetry; mean-field for N=3 yields intertwined orders and spin fragmentation with liquid orbitals.
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Quadratic-band-touching Hamiltonians in 2D possess USp(2N) symmetry; respecting interactions are limited to two terms that either preserve the symmetry or break it to USp(N) x USp(N), while lattice versions reduce to U(N) symmetry.
One-loop effective Lagrangian for Dirac fermions on a magnetic four-torus, with magnetization that can flip between paramagnetic and diamagnetic under twisted boundary conditions.
Charm and bottom quark masses are extracted as 1275.8 ± 0.4 MeV and 4177.0 ± 7.2 MeV using PMC-improved conformal series from quarkonium sum-rule moments, agreeing with PDG averages within 1σ.