Abstract

In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the “pseudo”-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as “order-by-disorder” fluctuations can lift the degeneracy and induce a gap for these modes. In this talk, I will discuss how these pseudo-Goldstone gaps arise in frustrated magnets when the fluctuations are (i) quantum mechanical and (ii) thermal in origin. I will show that the gap can be exactly computed at leading order using an effective picture where the soft modes move in a potential generated by the fluctuation-induced free energy. Using explicit interacting spin-wave calculations and direct numerical simulation, I will illustrate and validate this framework for several key models of order-by-disorder. Finally, I will discuss some implications for candidate materials exhibiting order-by-disorder.