Exceptional order-by-disorder phenomena in non-reciprocally frustrated systems

Recently, a surprising analogy was given between geometric frustration and non-reciprocal interactions. Systems with antisymmetric couplings will generically contain a set of marginal orbits, which can be regarded as a dynamical counterpart of an accidental ground state degeneracy [1]. Imperfections were shown to lift the “accidental degeneracy” analogous to the so-called order-by-disorder phenomenon known to occur in geometrically frustrated systems.

We demonstrate there are fundamental differences between the two types of frustration. We find that the ‘’accidental degeneracy” of orbits is characterized by an alignment of covariant Lyapunov vectors (CLVs), a generalization of the alignment of eigenvectors for non-Hermitian matrices commonly referred to as an exceptional point[2]. In contrast, the ground state of a geometrically frustrated system at equilibrium is characterized by orthogonal modes. Our work suggests that CLV alignment results in long relaxation times analogous to the traditional exceptional point. We further find an orbit-selection mechanism where systems that exhibit quasi-periodic orbits and chaos choose periodic orbits. The selection occurs irrespective of the fluctuation properties of the orbit distinct from the mechanism in geometrically frustrated systems.

[1] R. Hanai, arXiv:2208.08577

[2] C. Weis, et al., arXiv:2207.11667