Non-thermal excited-state quantum phase transitions

We report a kind of phase transition which takes place in isolated quantum systems with a discrete symmetry. Different phases are separated by a critical energy and recognized by means of an order parameter, which can be experimentally measured. Below the critical energy, the symmetry is broken and the equilibrium state is non-thermal, keeping large amounts of memory of the initial condition. Above, the symmetry is restored and a thermal equilibrium state is reached. We identify two universality classes, one showing a second-order phase transition and represented by the Lipkin-Meshkov-Glick model, and another showing a first-order phase transition and represented by the Dicke model. This work is dedicated to the memory of Joaquín Retamosa