Recently, we have numerically evaluated the current-current correlation function for the ground states of three-band models for the CuO planes of high-
Tc superconductors at hole doping
x=1∕8 using systems with 24 sites and periodic boundary conditions. In this paper, the numerical analysis is extended to a wider range of parameters. Our results show no evidence for the time-reversal symmetry violating current patterns recently proposed by Varma [C. M. Varma, Phys. Rev. B 73, 155113 (2006)]. If such current patterns exist, our results indicate that the energy associated with the loop currents must be smaller than
5meV per link even if the on-site chemical potential on the oxygen sites, which is generally assumed to be of the order of ${ϵ}_{\mathrm{p}}\ensuremath{-}{ϵ}_{\mathrm{d}}=3.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, is taken to 1.8, 0.9, 0.4, and finally
0eV. The current-current correlations remain virtually unaffected as we increase the interatomic Coulomb repulsion
Vpd, the term driving the system into the current carrying phase in Varma's analysis, from
1.2to2.4eV. Assuming that the three-band models are adequate, quantum critical fluctuations of such patterns hence cannot be responsible for phenomena occurring at significantly higher energies, such as superconductivity or the anomalous properties of the pseudogap phase. We further derive an upper bound for the magnetic moment per unit cell from the upper bound we obtain for spontaneous currents, and find it smaller than the magnetic moment measured in a recent neutron scattering experiment. In this context, we observe that if the observed magnetic moments were due to a current pattern, the magnitude of these currents would be insufficient to determine the phase diagram. Finally, we discuss the role of finite size effects in our numerical experiments. In particular, we show that the net spin
1∕2 of our finite size ground states does not infringe on the validity of our conclusions.
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudogaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the
d-wavelike pairing correlations in the hole-doped state, at least up to a doping of 10%. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders at low doping.
We study current-current correlations in the three-band Hubbard model for two-leg CuO ladders using the density-matrix renormalization group method. We find that these correlations decrease exponentially with distance for low doping but as a power law for higher doping. Their pattern is compatible with the circulating current (CC) phase which Varma has proposed to explain the pseudo-gaped metallic phase in underdoped high-temperature superconductors. However, for model parameters leading to a realistic ground state in the undoped ladder, the current fluctuations decay faster than the d-wave-like pairing correlations in the doped state. Thus we conclude that no phase with CC order or dominant CC fluctuations occur in the three-band model of two-leg CuO ladders.
We study a three-band effective model of a CuO 2 plane for the simple case of a single hole, with the aim of investigating the nature of the ground state stabilized by the motion of a single hole on the CuO 2 lattice. Our model is derived from, and retains the essential physics of the Anderson lattice model, but is more amenable to further investigation by virtue of the lifting of the spin degeneracy on the copper sites provided by perturbation theory. We use the Lanczos algorithm to numerically solve a series of finite systems which tend to the CuO 2 plane in the thermodynamic limit. Although we only study finite systems, the largest systems are sufficiently large to demonstrate behaviour that is independent of the boundary conditions, and is hence representative of the behaviour in the thermodynamic limit. In order to gain a good understanding of the competing energy scales, we consider only a single hole at T = 0. Our calculations predict that the ground state of the three-band model for a single hole is strongly quantum, dominated by short-range dimer correlations, reminiscent of a resonating valence bond state. There is no evidence for a discontinuity in the occupation number, indicating that the system is not a Fermi liquid. These predictions are in contrast to those of the t – J model, where the hole motion alone predicts Nagaoka ferromagnetism for the planar system, and one must include magnetic exchange terms in order to obtain the experimentally observed low-spin ground state.
The hole distribution within a
CuO2 plane, a common structural element of high-temperature superconductors, is investigated as a function of doping by holes. The correlated ground state of a three-band Hubbard model is found by making use of a local ansatz which includes local correlations between holes. It is found that doped holes have \ensuremath{\sim}70% oxygen character for the parameters determined from the local-density approximation, in agreement with experimental observations, while hole droplets on oxygen orbitals are formed for large copper-oxygen Coulomb repulsion,
Udp. All our results agree with those obtained from finite-cluster diagonalization.
Upon doping, Mott insulators often exhibit symmetry breaking where charge carriers and their spins organize into patterns known as stripes. For high-transition temperature cuprate superconductors, stripes are widely suspected to exist in a fluctuating form. We used numerically exact determinant quantum Monte Carlo calculations to demonstrate dynamical stripe correlations in the three-band Hubbard model, which represents the local electronic structure of the copper-oxygen plane. Our results, which are robust to varying parameters, cluster size, and boundary conditions, support the interpretation of experimental observations such as the hourglass magnetic dispersion and the Yamada plot of incommensurability versus doping in terms of the physics of fluctuating stripes. These findings provide a different perspective on the intertwined orders emerging from the cuprates' normal state.