Self-induced glassy phase in multimodal cavity quantum electrodynamics

We provide strong evidence that the effective spin-spin interaction in a multimodal confocal optical cavity gives rise to a self-induced glassy phase, which emerges exclusively from the peculiar euclidean correlations and is not related to the presence of disorder as in standard spin glasses. As recently shown, this spin-spin effective interaction is both non-local and non-translational invariant, and randomness in the atoms positions produces a spin glass phase. Here we consider the simplest feasible disorder-free setting where atoms form a one-dimensional regular chain and we study the thermodynamics of the resulting effective Ising model. We present extensive results showing that the system has a low-temperature glassy phase. Notably, for rational values of the only free adimensional parameter $\alpha=p/q$ of the interaction, the number of metastable states at low temperature grows exponentially with $q$ and the problem of finding the ground state rapidly becomes computationally intractable, suggesting that the system develops high energy barriers and ergodicity breaking occurs.