Fictive Impurity Approach to Dynamical Mean Field Theory: a Strong-Coupling Investigation

Quantum Monte Carlo and semiclassical methods are used to solve two and four site cluster dynamical mean field approximations to the square lattice Hubbard model at half filling and strong coupling. The energy, spin correlation function, phase boundary and electron spectral function are computed and compared to available exact results. The comparision permits a quantitative assessment of the ability of the different methods to capture the effects of intersite spin correlations. Two real space methods and one momentum space representation are investigated. One of the two real space methods is found to be significantly worse: in it, convergence to the correct results is found to be slow and, for the spectral function, nonuniform in frequency, with unphysical midgap states appearing. Analytical arguments are presented showing that the discrepancy arises because the method does not respect the pole structure of the self energy of the insulator. Of the other two methods, the momentum space representation is found to provide the better approximation to the intersite terms in the energy but neither approximation is particularly acccurate and the convergence of the momentum space method is not uniform. A few remarks on numerical methods are made.Comment: Errors in previous versions corrected; CDMFT results adde

On the Bilayer Coupling in the Yttrium-Barium Family of High Temperature Superconductors

We present and solve a model for the susceptibility of two CuO2 planes coupled by an interplane coupling J_perp and use the results to analyze a recent "cross-relaxation" NMR experiment on Y2Ba4Cu7O15. We deduce that in this material the product of J_perp and the maximum value of the in-plane susceptibility chi_max varies from approximately 0.2 at T = 200 K to 0.4 at T = 120 K and that this implies the existence of a temperature dependent in-plane spin correlation length. Using estimates of chi_max from the literature we find 5 meV < J_perp < 20 meV. We discuss the relation of the NMR results to neutron scattering results which have been claimed to imply that in YBa2Cu3O_{6+x} the two planes of a bilayer are perfectly anticorrelated. We also propose that the recently observed 41 meV excitation in YBa2Cu3O7 is an exciton pulled down below the superconducting gap by J_perp.Comment: 11 pages, 3 postscript figures (uuencoded and compressed

Spin Gaps and Bilayer Coupling in YBa2_2Cu3_3O7−δ_{7-\delta} and YBa2_2Cu4_4O8_8

We investigate the relevance to the physics of underdoped YBa$_2$Cu$_3$O$_{\rm 6+x}$ and YBa$_2$Cu$_4$O$_8$ of the quantum critical point which occurs in a model of two antiferromagnetically coupled planes of antiferromagnetically correlated spins. We use a Schwinger boson mean field theory and a scaling analysis to obtain the phase diagram of the model and the temperature and frequency dependence of various susceptibilities and relaxation rates. We distinguish between a low $\omega ,T$ coupled-planes regime in which the optic spin excitations are frozen out and a high $\omega ,T$ decoupled-planes regime in which the two planes fluctuate independently. In the coupled-planes regime the yttrium nuclear relaxation rate at low temperatures is larger relative to the copper and oxygen rates than would be naively expected in a model of uncorrelated planes. Available data suggest that in YBa$_2$Cu$_4$O$_8$ the crossover from the coupled to the decoupled planes regime occurs at $T 700K$ or $T \sim 200K$. The predicted correlation length is of order 6 lattice constants at $T=200K$. Experimental data related to the antiferromagnetic susceptibility of YBa$_2$Cu$_4$O$_8$ may be made consistent with the theory, but available data for the uniform susceptibility are inconsistent with the theory.Comment: RevTex 3.

Fictive Impurity Models: an Alternative Formulation of the Cluster Dynamical Mean Field Method

"Cluster" extensions of the dynamical mean field method to include longer range correlations are discussed. It is argued that the clusters arising in these methods are naturally interpreted not as actual subunits of a physical lattice but as algorithms for computing coefficients in an orthogonal function expansion of the momentum dependence of the electronic self-energy. The difficulties with causality which have been found to plague cluster dynamical mean field methods are shown to be related to the "ringing" phenomenon familiar from Fourier analysis. The analogy is used to motivate proposals for simple filtering methods to circumvent them. The formalism is tested by comparison to low order perturbative calculations and self consistent solutions

Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: shadow and flat bands

We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, $\chi (q, \omega)$, and to the quasiparticle spectral function function, $A(k, \omega)$, are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for $\chi(q, \omega)$ and an approximate solution for $A(k, \omega)$. We show that (i) $A(k)$ at a given, small $\omega$ has an extra peak at $k = k_F + \pi$ (`shadow band'), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.Comment: a sign and amplitude of the vertex renormalization and few typos are correcte

Effects of intrabilayer coupling on the magnetic properties of YBa2_2Cu3_3O6_6

A two-layer Heisenberg antiferromagnet is studied as a model of the bilayer cuprate YBa$_2$Cu$_3$O$_6$. Quantum Monte Carlo results are presented for the temperature dependence of the spin correlation length, the static structure factor, the magnetic susceptibility, and the $^{63}$Cu NMR spin-echo decay rate $1/T_{2G}$. As expected, when the ratio $J_2/J_1$ of the intrabilayer and in-plane coupling strengths is small, increasing $J_2$ pushes the system deeper inside the renormalized classical regime. Even for $J_2/J_1$ as small as $0.1$ the correlations are considerably enhanced at temperatures as high as $T/J_1 \approx 0.4-0.5$. This has a significant effect on $1/T_{2G}$, and it is suggested that measurements of this quantity at high temperatures can reveal the strength of the intrabilayer coupling in YBa$_2$Cu$_3$O$_6$.Comment: 10 pages (Revtex) + 5 uuencoded ps figures. To appear in Phys. Rev. B, Rapid Com

Coexistence of Superconductivity and Antiferromagnetism in Multilayered High-TcT_c Superconductor HgBa2_2Ca4_4Cu5_5Oy_y: A Cu-NMR Study

We report a coexistence of superconductivity and antiferromagnetism in five-layered compound HgBa$_2$Ca$_4$Cu$_5$O$_y$ (Hg-1245) with $T_c=108$ K, which is composed of two types of CuO$_2$ planes in a unit cell; three inner planes (IP's) and two outer planes (OP's). The Cu-NMR study has revealed that the optimallydoped OP undergoes a superconducting (SC) transition at $T_c=108$ K, whereas the three underdoped IP's do an antiferromagnetic (AF) transition below $T_N\sim$ 60 K with the Cu moments of $\sim (0.3-0.4)\mu_B$. Thus bulk superconductivity with a high value of $T_c=108$ K and a static AF ordering at $T_N=60$ K are realized in the alternating AF and SC layers. The AF-spin polarization at the IP is found to induce the Cu moments of $\sim0.02\mu_B$ at the SC OP, which is the AF proximity effect into the SC OP.Comment: 6 pages, 8 figure

NMR and Neutron Scattering Experiments on the Cuprate Superconductors: A Critical Re-Examination

We show that it is possible to reconcile NMR and neutron scattering experiments on both LSCO and YBCO, by making use of the Millis-Monien-Pines mean field phenomenological expression for the dynamic spin-spin response function, and reexamining the standard Shastry-Mila-Rice hyperfine Hamiltonian for NMR experiments. The recent neutron scattering results of Aeppli et al on LSCO (x=14%) are shown to agree quantitatively with the NMR measurements of $^{63}T_1$ and the magnetic scaling behavior proposed by Barzykin and Pines. The reconciliation of the $^{17}T_1$ relaxation rates with the degree of incommensuration in the spin fluctuation spectrum seen in neutron experiments is achieved by introducing a new transferred hyperfine coupling $C'$ between oxygen nuclei and their next nearest neighbor $Cu^{2+}$ spins; this leads to a near-perfect cancellation of the influence of the incommensurate spin fluctuation peaks on the oxygen relaxation rates of LSCO. The inclusion of the new $C'$ term also leads to a natural explanation, within the one-component model, the different temperature dependence of the anisotropic oxygen relaxation rates for different field orientations, recently observed by Martindale $et~al$. The measured significant decrease with doping of the anisotropy ratio, $R= ^{63}T_{1ab}/^{63}T_{1c}$ in LSCO system, from $R =3.9$ for ${\rm La_2CuO_4}$ to $R ~ 3.0$ for LSCO (x=15%) is made compatible with the doping dependence of the shift in the incommensurate spin fluctuation peaks measured in neutron experiments, by suitable choices of the direct and transferred hyperfine coupling constants $A_{\beta}$ and B.Comment: 24 pages in RevTex, 9 figures include

Exact Results for the Crossover from Gaussian to Non-Gaussian Order Parameter Fluctuations in Quasi One-Dimensional Electronic Systems

The physics of quasi one-dimensional Peierls systems is dominated by order parameter fluctuations. We present an algorithm which allows for the first time to exactly calculate physical properties of the electrons gas coupled to classical order parameter fluctuations. The whole range from the Gaussian regime dominated by amplitude fluctuations to the non-Gaussian regime dominated by phase fluctuations is accessible. Our results provide insight into the 'pseudogap' phenomenon occurring in underdoped high-temperature superconductors, quasi one-dimensional organic conductors and liquid metals.Comment: 4 pages, 4 figures, accepted for publication in Physical Review Letter

Charge degree of freedom and single-spin fluid model in YBa_2Cu_4O_8

We present a 17O nuclear magnetic resonance study in the stoichiometric superconductor YBa_2Cu_4O_8. A double irradiation method enables us to show that, below around 180 K, the spin-lattice relaxation rate of plane oxygen is not only driven by magnetic, but also significantly by quadrupolar fluctuations, i.e. low-frequency charge fluctuations. In the superconducting state, on lowering the temperature, the quadrupolar relaxation diminishes faster than the magnetic one. These findings show that, with the opening of the pseudo spin gap, a charge degree of freedom of mainly oxygen character is present in the electronic low-energy excitation spectrum.Comment: 4 pages, 3 figures, REVTE