Generic "Unnecessary" Quantum Critical Points
Quantum phase transitions can host much richer and more exotic phenomena compared with classical phase transitions. One of the examples is the generic "unnecessary" quantum critical points. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but all the deformations are irrelevant perturbations below certain threshold at the quantum critical points. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). Unnecessary quantum critical points are directly related to the classification of interacting topological insulators. Motivated from the recently discussed valley Chern insulators in Moiré systems, we identify unusual examples of topological insulators, whose classification under interaction is very different from previously known cases. These examples give us generic unnecessary quantum critical points with minimal degrees of freedom.