Abstract

Having conflicting goals often leads to frustration. The conflict occurs, for example, in systems that cannot simultaneously minimize all interaction energy between the constituents, a situation known as geometrical frustration. A typical feature of these systems is the presence of accidental ground state degeneracy that gives rise to a rich variety of unusual phenomena such as order-by-disorder and spin glasses. In this talk, I will show that a dynamical counterpart of these phenomena may arise from a fundamentally different, non-equilibrium source of conflict: non-reciprocal interactions [1]. I will show that non-reciprocal systems with anti-symmetric coupling generically generate marginal orbits that can be regarded as a dynamical counterpart of accidental degeneracy, due to the emerging Liouvilletype theorem. These “accidental degeneracies” of orbits are shown to often get “lifted” by stochastic noise or weak random disorder to give rise to order-by-disorder phenomena with the peculiarity that the emerging state usually has a time crystalline order. I further report numerical evidence of a non-reciprocity-induced spin-glass-like state that exhibits aging and a power-law temporal relaxation associated with a short-ranged spatial correlation. This work provides an unexpected link between the physics of complex magnetic materials and non-reciprocal matter.   [1] R. Hanai, arXiv:2208.08577.