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 $\ensuremath{\delta}=1\ensuremath{-}n).$ We show that the ETT point $(\ensuremath{\delta}={\ensuremath{\delta}}_{c}, T=0)$ 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 $(T=0, \ensuremath{\delta}>{\ensuremath{\delta}}_{c})$ 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 ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}J$ model.) The anomalies take place on one side of the ETT $(\ensuremath{\delta}<{\ensuremath{\delta}}_{c}$ in the case of ${t}^{\ensuremath{'}}/t<0$ corresponding to the high-
Tc cuprates) and have a striking similarity with the anomalies observed in the high-
Tc 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, ${T}^{*}(\ensuremath{\delta})\ensuremath{\propto}{\ensuremath{\delta}}_{c}\ensuremath{-}\ensuremath{\delta},$ which grows from the point $\ensuremath{\delta}={\ensuremath{\delta}}_{c}$ on the side $\ensuremath{\delta}<{\ensuremath{\delta}}_{c}.$ 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).
We systematically examine the asymmetry of the electronic states in the hole- and electron-doped cuprates by using a $t\text{\ensuremath{-}}J$ model with the second-neighbor hopping ${t}^{\ensuremath{'}}$ and third one ${t}^{\ensuremath{''}}$ (the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model). Numerically exact diagonalization method is employed for a 20-site square lattice. We impose twisted boundary conditions (BC) instead of standard periodic BC. For static and dynamical correlation functions, averaging procedure over the twisted BC is used to reduce the finite-size effect. We find that antiferromagnetic spin correlation remains strong in electron doping in contrast to the case of hole doping, being similar to the case of the periodic BC. This leads to a remarkable electron-hole asymmetry in the dynamical spin structure factor and two-magnon Raman scattering. By changing the twist, the single-particle spectral function is obtained for all momenta in the Brillouin zone. Examining the spectral function in detail, we find a gap opening at around the $\mathbf{k}=(\ensuremath{\pi},0)$ region for 10% doping of holes (the carrier concentration
x=0.1), leading to a Fermi arc that is consistent with experiments. In electron doping, however, a gap opens at around $\mathbf{k}=(\ensuremath{\pi}∕2,\ensuremath{\pi}∕2)$ and persists up to
x=0.2, being correlated with the strength of the antiferromagnetic correlation. We find that the magnitude of the gaps is sensitive to ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$. A pseudogap is also seen in the optical conductivity for electron doping, and its magnitude is found to be the same as that in the spectral function. We compare calculated quantities with corresponding experimental data, and discuss similarities and differences between them as well as their implications.
We use a variational approach to gain insight into the strongly correlated
d-wave superconducting state of the high
Tc cuprates at
T=0. We show that strong correlations lead to qualitatively different trends in pairing and phase coherence: the pairing scale decreases monotonically with hole doping while the superconducting order parameter shows a nonmonotonic dome. We obtain detailed results for the doping dependence of a large number of experimentally observable quantities, including the chemical potential, coherence length, momentum distribution, nodal quasiparticle weight and dispersion, incoherent features in photoemission spectra, optical spectral weight, and superfluid density. Most of our results are in remarkable quantitative agreement with existing data and some of our predictions, first reported in Phys. Rev. Lett. 87, 217002 (2001), have been recently verified.
With high-Tc cuprates in mind, properties of correlated dx2-y2-wave superconducting (SC) and antiferromagnetic (AF) states are studied for the Hubbard (t-t'-U) model on square lattices, using a variational Monte Carlo method. We employ simple trial wave functions including only crucial parameters, such as a doublon-holon binding factor indispensable to describe correlated SC and normal states as doped Mott insulators. U/t, t'/t and δ(doping rate) dependence of relevant quantities are systematically calculated. As U/t increases, a sharp crossover of SC properties occurs at U_co/t \sim 10 from a conventional BCS type to a kinetic-energy-driven type for any t'/t. As δdecreases, U_co/t is smoothly connected to the Mott transition point at half filling. For U/t\lsim 5, steady superconductivity corresponding to the cuprates is not found, whereas the d-wave SC correlation function Pd^\infty rapidly increases for U/t\gsim 6 and becomes maximum at U=U_co. Comparing the δdependence of Pd^\infty with experimentally observed dome-shaped Tc and condensation energy, we find that the effective value of
U for the cuprates should be larger than the band width, for which the t-J model is valid. Analyzing the kinetic energy, we reveal that for U>U_co only doped holes (electrons) become charge carriers, which will make a small Fermi surface (hole pocket), but for UU_co is determined by two factors, i.e., the AF spin correlation, which creates singlet pairs (pseudogap), and the charge mobility dominated by Mott physics.
Quantum Monte Carlo (QMC) and maximum-entropy techniques are used to study the spectral function $A(\mathbf{p},\ensuremath{\omega})$ of the one-band Hubbard model with strong coupling including a next-nearest-neighbor electronic hopping with amplitude ${t}^{\ensuremath{'}}/t=\ensuremath{-}0.35$. These values of parameters are chosen to improve the comparison of the Hubbard model with angle-resolved photoemission (ARPES) data for
Sr2CuO2Cl2. A narrow quasiparticle (qp) band is observed in the QMC analysis at the temperature of the simulation
T=t/3, both at and away from half-filling. Such a narrow band produces a large accumulation of weight in the density of states at the top of the valence band. As the electronic density
〈n〉 decreases further away from half-filling, the chemical potential travels through this energy window with a large number of states, and by $〈n〉\ensuremath{\sim}0.70$ it has crossed it entirely. The region near momentum $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ in the spectral function is more sensitive to doping than momenta along the diagonal from
(0,0) to $(\ensuremath{\pi},\ensuremath{\pi})$. The evolution with hole density of the quasiparticle dispersion contains some of the features observed in recent ARPES data in the underdoped regime. For sufficiently large hole densities the ``flat'' bands at $(\ensuremath{\pi},0)$ cross the Fermi energy, a prediction that could be tested with ARPES techniques applied to overdoped cuprates. The population of the qp band introduces a hidden density in the system which produces interesting consequences when the quasiparticles are assumed to interact through antiferromagnetic fluctuations and studied with the BCS gap-equation formalism. In particular, a region of extended
s-wave character is found to compete with the
d wave in the overdoped regime, i.e., when the chemical potential has almost entirely crossed the qp band as
〈n〉 is reduced. The present study also shows that previous ``real-space'' pairing theories for the cuprates, such as the antiferromagnetic Van Hove scenario, originally constructed based on information gathered at half-filling, do not change their predictions if hole dispersions resembling noninteracting electrons with renormalized parameters are used.