Non-reciprocal frustration induced order-by-disorder and spin-glass-like state

In this talk, I will draw an unexpected link between two concepts that, at a glance, do not seem to have anything to do with each other: geometrical frustration and non-reciprocal interactions [1]. I show that exotic phenomena that are known to occur in systems with the former can also occur in the latter.

A well-known source of frustration in equilibrium is what is known as geometrical frustration. The salient feature of systems with geometrical frustration is that they often exhibit accidental degeneracy of ground states, which is what gives rise to unusual phenomena such as order-by-disorder and spin glasses. In this talk, I will show that a dynamical counterpart of these phenomena arises from a conceptionally different, nonequilibrium source of conflict: non-reciprocal interaction. This is based on the observation that systems with anti-symmetric non-reciprocal coupling generically exhibit marginal orbits due to the emergence of the Liouville-type theorem, which can be regarded as a dynamical counterpart of accidentally degenerate ground states. I show that these “accidentally degenerate” orbits are generically “lifted” by stochastic noise or weak random disorder, to give rise to order-by-disorder phenomena (but typically with time crystalline order in my non-reciprocal case). I further numerically show that a state reminiscent of spin glasses emerges, which exhibits slow dynamics with temporal power-law decay and aging but with spatially short-ranged correlation.

[1] R. Hanai, arXiv:2208.08577