Altermagnetic Ground States on the Ammann--Beenker Tiling

Abstract

We identify exact altermagnetic ground states of a classical Heisenberg model on a quasicrystal. Considering the Ammann--Beenker tiling as an example, we determine the ground states by exploiting the parity structure of its parent four-dimensional hypercubic lattice. The ground state hosts coplanar altermagnetic order characterized by the preserved spin-group symmetry $[C_{2x}\parallel C_{8z}]$. Without translational symmetry, the momentum-space spin splitting that usually identifies altermagnets is not directly accessible. We instead couple the spins to itinerant electrons and show spin-resolved transport with $g$-wave symmetry, confirming the altermagnetic nature in a nonperiodic system. Our results establish a geometric route to altermagnetic order in quasicrystals, connecting exact magnetic ground states to their spin-resolved transport signatures.