Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T_c cuprates' phase diagram. There are at least two distinct proposals on the critical concentration and its physical origin. First one is associated with the pseudogap formation for p<p*, with p~0.2. Another one relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p_{opt}~0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.
@article{arxiv.0908.0576,
title = {From underdoped to overdoped cuprates: two quantum phase transitions},
author = {S. G. Ovchinnikov and E. I. Shneyder and M. M. Korshunov},
journal= {arXiv preprint arXiv:0908.0576},
year = {2015}
}