Emergent symmetry at transition between intertwined vestigial orders in iron-based superconductors*

The phase diagram of iron-based superconductors consists of various electronic orders, including antiferromagnetic and symmetry related vestigial orders. They are highly entangled with superconductivity. Here we unveil the hidden Lie algebra among the nematic, charge C₄, and chiral C₄ vestigial orders. We further show that, because of the intertwined nature of these order parameters, the system exhibits an emergent U(1) symmetry at the first-order transition between the nematic and charge C₄ phases. This enriched continuous symmetry

gives rise to a Goldstone mode at the transition point and causes softening of excitations in the nematic and charge sectors when the system is close to the transition. We discuss ways to probe these effects in experiments and the implications of our results for iron-based superconductors and other correlated systems.