A Mermin-Wagner theorem violation: Non-markovianity enabling long-range order in low dimensions

It is now well established that the Mermin-Wagner theorem can be violated out of equilibrium, allowing long-range order through the spontaneous symmetry breaking of a continuous symmetry. However, the few models where this has been proven typically require either convection or anisotropies—conditions that are not always realisable/desirable in condensed matter systems. In this talk, I'll discuss the existence of a new class of O(N)-symmetric models that has potential to violate the Mermin-Wagner theorem thus allowing long-range order in low spatial dimensions, due to a combination of non-markovian dynamics, non-equilibrium conditions, and the presence of conserved quantities. I will also discuss how this models could be realized in quantum simulation platforms capable of simulating spin systems (e.g., Rydberg atoms) or bosonic systems (e.g., ultracold atoms, exciton-polaritons).