Quantum critical point associated with the electronic topological transition in a two-dimensional electron system as a driving force for anomalies in underdoped high-Tc cuprates

We study an electronic topological transition (ETT) (the transition due to change in topology of Fermi surface) that occurs in a two-dimensional electron system on a square lattice with hopping beyond nearest neighbors under a change of electronic concentration n (or of hole doping delta=1-n). We show that the ETT point (delta = delta(c), T=0) is an exotic quantum critical point (QCP) with several aspects of criticality. The first trivial one is related to singularities in thermodynamic properties. A nontrivial and never considered aspect concerns a behavior of the electron-hole response function: the ETT point is a quantum multicritical point, the end point of the critical line (T=0, delta>delta(c)) of static Kohn singularities. We show that the existence of this QCP results in global anomalies of the system in the presence of interaction. (We consider the interaction corresponding to the t-t'-J model.) The anomalies take place on one side of the ETT (delta<delta(c) in the case of t'/t<0 corresponding to the high-T-c cuprates) and have a striking similarity with the anomalies observed in the high-T-c cuprates in the underdoped regime. The most important consequence of the ETT(besides the appearance of superconducting instability of the d-wave symmetry) is the existence of the pseudocritical zone, T* (delta) proportional to delta(c)- delta, which grows from the point delta=delta(c) on the side delta<delta(c). Below and around this zone the metal state is anomalous. Some anomalies are considered in the present paper and compared with experiment (NMR, neutron scattering).