Emergent Symmetries in the Classical Γ'-Model

Magnetic frustration can induce a wide range of fascinating phenomena beyond conventional magnetic order. In classical magnetic systems, one of its most striking manifestations is in the formation of non-trivial ground-state manifolds. For example, the degeneracy of the ground state manifold may in fact be accidental, unrelated to any underlying symmetry of the Hamiltonian but rather giving rise to a new emergent symmetry. A number of disparate models, in two and three dimensions, have been shown to exhibit such emergent symmetries. In this talk, we will show that the bond-anisotropic and symmetric off-diagonal exchange interaction, the Γ'-model (Gamma-prime), exhibits a continuous emergent U(1) symmetry at the level of a single triangle. By combining such triangles together to form full lattices, of corner or edge-sharing triangles, according to a simple set of rules this emergent symmetry can be maintained. This allows for a systematic study of the interplay between this emergent continuous U(1) symmetry and the underlying discrete Hamiltonian symmetries in different lattices across one, two, and three dimensions. We will discuss the impact of thermal and quantum fluctuations in lifting the accidental ground state degeneracy via the thermal and quantum order-by-disorder mechanisms, and how spatial dimensionality and lattice symmetries play a crucial role in shaping the physics of the model.