Exceptional rings protected by emergent symmetry for mechanical systems

We propose mechanical systems, described by Newton's equation of motion, as suited platforms for symmetry protection of non-Hermitian degeneracies. We point out that in contrast to other systems with gain and loss, fine tuning of parameters is not required to realize symmetry-protected non-Hermitian degeneracies due to an emergent property of mechanical systems. The presence of symmetry-protected exceptional rings with extended chiral symmetry is numerically demonstrated for a mechanical graphene with friction. Furthermore, classification of symmetry-protected non-Hermitian degeneracies is addressed by taking into account the emergent properties of mechanical systems.