Motivated by the recent report of broken time-reversal symmetry and zero momentum magnetic scattering in underdoped cuprates, we investigate under which circumstances orbital currents circulating inside a unit cell might be stabilized in extended Hubbard models that explicitly include oxygen orbitals. Using Gutzwiller projected variational wave functions that treat on an equal footing all instabilities, we show that orbital currents indeed develop on finite clusters and that they are stabilized in the thermodynamic limit if additional interactions, e.g., strong hybridization with apical oxygens, are included in the model.
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 the phase diagram of an effective three-orbital model of the cuprates using variational Monte Carlo calculations on asymptotically large lattices and exact diagonalization on a 24-site cluster. States with ordered orbital current loops (LC), itinerant antiferromagnetism, d-wave superconductivity, and the Fermi liquid are investigated using appropriate Slater determinants refined by Jastrow functions for on-site and intersite correlations. We find an LC state stable in the thermodynamic limit for a range of parameters compatible with the Fermi surface of a typical hole doped superconductor provided the transfer integrals between the oxygen atoms have signs determined by the effects of indirect transfer through the Cu-4s orbitals as suggested by Andersen. The results of the calculations are that the LC phase gives way at lower dopings to an antiferromagnetism phase, and at larger dopings to superconductivity and Fermi liquid phases.
We investigate the magnetic orders and excitations in a half-filled Hubbard model that continuously interpolates between the Lieb and kagome lattices. Using the self-consistent Hartree-Fock approximation combined with the Bethe-Salpeter equation in the random phase approximation, we map the U − t ′ phase diagram of the Lieb-kagome lattices and compute real-frequency transverse spin susceptibilities, i.e., the magnon spectra. Dynamical mean-field theory and exact diagonalization are used as complementary checks of static magnetic phases. In particular, besides gapless Goldstone magnons, the symmetry-broken ferrimagnetic and antiferromagnetic phases also exhibit gapped Higgs magnon bands, which originate from amplitude fluctuations in the order parameter characterizing spontaneous symmetry breaking.
We introduce the generalization of the slave-spin mean-field method to broken-symmetry phases. Through a variational approach we derive the single-particle energy shift in the mean-field equations which generates the appropriate self-consistent field responsible for the stabilization of the broken symmetry. With this correction the different flavors of the slave-spin mean field are actually the same method and they give identical results to Kotliar-Ruckenstein slave bosons and to the Gutzwiller approximation. We apply our formalism to the N\'eel antiferromagnetic state and study it in multiorbital models as a function of the number of orbitals and Hund's coupling strength, providing phase diagrams in the interaction-doping plane. We show that the doped antiferromagnet in proximity of half filling is typically unstable toward insulator-metal and magnetic-nonmagnetic phase separation. Hund's coupling extends the range of this antiferromagnet, and favors its phase separation.
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.