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We develop an exactly solvable model with Kitaev-type interactions and study its phase diagram on the dual lattice of the quasicrystalline Ammann-Beenker lattice. Our construction is based on the $\Gamma$-matrix generalization of the Kitaev model and utilizes the cut-and-project correspondence between the four-dimensional simple cubic lattice and the Ammann-Beenker lattice to designate four types of bonds. We obtain a rich phase diagram with gapped (chiral and abelian) and gapless spin liquid phases via Monte Carlo simulations and variational analysis. We show that the ground state can be further tuned by the inclusion of an onsite term that selects 21 different vison configurations while maintaining the integrability of the model. Our results highlight the rich physics at the intersection of quasicrystals and quantum magnetism.

The proposed topological Kondo insulator SmB$_{6}$ hosts a bulk Kondo hybridization gap that stems from strong electronic correlations and a metallic surface state whose effective mass remains disputed. Thermopower and scanning tunneling spectroscopy measurements argue for heavy surface states that also stem from strong correlations, whereas quantum oscillation and angle-resolved photoemission measurements reveal light effective masses that would be consistent with a Kondo breakdown scenario at the surface. Here we investigate the evolution of the surface state via electrical and thermoelectric transport measurements under hydrostatic pressure, a clean symmetry-preserving tuning parameter that suppresses the Kondo gap and increases the valence of Sm from 2.6+ towards a 3+ magnetic metallic state. Electrical resistivity measurements reveal that the surface carrier density increases with increasing pressure, whereas thermopower measurements show an unchanged Fermi energy under pressure. As a result, the effective mass of the surface state charge carriers linearly increases with pressure as the Sm valence approaches 3+. Our results are consistent with the presence of correlation-driven surface states in SmB$_{6}$ and suggest that the surface Kondo effect persists under pressure to 2 GPa.

Spontaneous magnetic order is a routine instance in three-dimensional (3D) materials but for a long time, it remained elusive in the 2D world. Recently, the first examples of (stand-alone) 2D van der Waals (vdW) crystals with magnetic order, either antiferromagnetic or ferromagnetic, have been reported. In this review, we describe the state of the art of the nascent field of magnetic 2D materials focusing on synthesis, engineering, and theory aspects. We also discuss challenges and some of the many different promising directions for future work.