As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ground state breaks the symmetry.
But what about the opposite case of SSB? The ground state of a quantum system possesses some kind of symmetry while the Hamiltonian does not have this symmetry. For example, the exactly solvable Kitaev-type model Hamiltonians explicitly break the spin rotational symmetry, but the ground states are spin liquids, which possess the spin rotational symmetry.
I wonder whether this opposite case of SSB plays an important role like SSB in physics?
Erratum: The example of "Kitaev model" I gave above is not correct, please see Why we call the ground state of Kitaev model a Spin Liquid? for the reason.
Examples with exact emergent symmetries:
A simple example with exact emergent $SU(2)$ spin-rotation symmetry can be found here A simple model that exhibits emergent symmetry?
Another example with exact emergent $U(1)$ symmetry is presented in the Supplemental Material of this paper, where it is appeared on page 2 under Eq.(A7).
Examples with approximate emergent symmetries:
The example with approximate emergent lattice 3-fold rotation symmetry is the existence of Ferromagnetic(FM) ground state in the Kitaev-Heisenberg model, where the model Hamiltonian explicitly breaks the lattice 3-fold rotation symmetry but the FM phase possesses the lattice 3-fold rotation symmetry.
Another example with emergent chiral symmetry was proposed by X.G.Wen in his paper, as seen on page 18, title C.
A third example with emergent time-reversal symmetry can be found here.
An example with an emergent global topological U(1) symmetry is presented here.
More examples with emergent symmetries are welcome.