Session J11 - HTSC Theory V: General Theory II.
MIXED session, Wednesday morning, March 19
Room 1202B, Conv. Center

[J11.01] Spin dynamics and exchange interactions in the Hubbard model

Basic approximations leading to the spin dynamics equations of Ref.1 are analyzed in the framework of the Hubbard model. A new version of Hubbard-Stratonovich transformation is proposed including the integration over the SU group. The derivation of the "classical" equations of motion for spin variables is based on the separation of "fast" and "slow" variables in the functional integral, neglecting of spin flip processes in the local coordinate system, and the use of the static approximation for the "potential" part of the effective spin Hamiltonian. The "kinetic" part appears as the Berry phase. Various contributions to the exchange interactions in the narrow band Hubbard model are analyzed. The case of the Hubbard model on the Bethe lattice Ref.2 is considered in details. Non-Heisenberg exchange interactions and phase separation in the almost-half-filled narrow band Hubbard model are considered. [1] V.P.Antropov,M.I.Katsnelson,M.van Schilfgaarde and B.N.Harmon. Phys.Rev.B,54,1019 (1996) [2] M.I.Auslender,M.I.Katsnelson.Teor.Mat.Fiz.51,436 (1982)

[J11.02] Low-Energy Excitation Properties of the Two-Dimensional Hubbard Model

Since the discovery of the high-Tc superconductivity, the nature of the low-energy excitation of two-dimensional systems has been one of central issues of condenced matter physics. From diagramatic studies of the two-dimensional Hubbard model, it is obtained that the imaginary part of the self-energy is proportional to \epsilon^2\log\epsilon, and the Fermi-liquid picture is considered to be valid. On contrary to this result, Anderson proposed that the forward scattering plays critical roles leading to the breakdown of the Fermi-liquid. We have calculated the self-energy in the t-matrix approximation, and have studied effects of the forward scattering process in detail. Based on this calculation, we report on the low-energy excitation properties of the two-dimensional Hubbard model.

[J11.03] Rapid suppression of spin gap in Zn-doped CuGeO_3 and SrCu_2O_3

The influence of non-magnetic impurities on the spectrum and dynamical spin structure factor of a model for CuGeO_3 is studied. A simple extension to Zn-doped Sr Cu_2 O_3 is also discussed. Using Exact Diagonalization techniques and intuitive arguments we show that Zn-doping introduces states in the Spin-Peierls gap of CuGeO_3(G. B. Martins, E. Dagotto, and J. Riera, to appear in Phys. Rev. B.). This effect can be understood easily in the large dimerization limit where doping by Zn creates ``loose'' S=1/2 spins, which interact with each other through very weak effective antiferromagnetic couplings. When the dimerization is small, a similar effect is observed but now with the free S=1/2 spins being the resulting S=1/2 ground state of severed chains with an odd number of sites. Experimental consequences of these results are discussed. It is interesting to observe that the spin correlations along the chains are enhanced by Zn-doping according to the numerical data presented here\footnotemark[1]^,(G. B. Martins, M. Laukamp, J. Riera, and E. Dagotto, preprint.). Similar arguments apply to ladders with non-magnetic impurities simply replacing the tendency to dimerization in CuGeO_3 by the tendency to form spin-singlets along the rungs in SrCu_2O_3\footnotemark[1]^,(Y. Motome, N. Katoh, N. Furukawa, and M. Imada, preprint.).

[J11.04] Dynamical Quantities of the Disordered, Attractive 2D Hubbard Model via Quantum Monte Carlo Simulations

The two-dimensional, attractive Hubbard Model has been used to explore qualitative features of the superconducting phase transition in strongly correlated electron systems. At half-filling, this model exhibits simultaneous charge density wave and superconducting order. Site disorder is known to break this symmetry, destroying charge ordering immediately and, at a finite value of the disorder, destroying the superconducting order as well. Using analytic continuation via maximum entropy techniques, we calculate for the first time from Quantum Monte Carlo simulations various dynamical quantities related to this disorder-driven phase transition. We specifically focus on the destruction of the superconducting gap in this model.

[J11.05] Spin And Charge Correlations of a Disordered Hubbard Model

The two dimensional Hubbard Hamiltonian is known to have long range magnetic order in its ground state at half-filling. At the same time, a Mott gap exists in the charge excitations. It is believed that understanding these correlations may be important in developing an electronic mechanism for superconductivity. Here we use Quantum Monte Carlo simulations to determine the effect of disordering the Hubbard model by setting the on-site repulsion U to zero on a fraction f of the sites. We find that magnetic order survives out to a critical concentration f_c of impurities, but that the Mott gap at half filling is immediately destroyed. Interestingly, the square of the ground state antiferromagnetic order parameter appears initially to be enhanced by disorder. We discuss the nature of the state at half-filling, ie whether or not it is metallic, as well as the Mott state which arises off half-filling, at a density n=1+f. Finally, we compare our findings with results from dynamical mean-field theory (limit of high dimensions).

[J11.06] Screening of Long-Range Coulomb Interactions in Hubbard Electron Systems

We present a hybrid approach for estimating the screening of extended Coulomb interactions in strongly correlated Hubbard electron systems which combines quantum Monte Carlo (QMC) and diagrammatic methods. The basic idea of this approach is to treat the strong local Hubbard-U repulsion exactly by QMC simulation of the standard, on-site-U Hubbard model and to incorporate these simulational results into an approximate RPA-type diagrammatic treatment of the much weaker long-range V-term. Renormalization of the total dielectric function in a real material due to the non-Hubbard filled-band electronic background and due to phonons can be included at the same level of approximation. Applications to estimate the screened near-neighbor Coulomb V in cuprate high-T_c systems and implications for d-wave and other spatially extended superconducting pairing mechanisms will be discussed.

[J11.07] Superconductivity in two component fermion system with attraction

The mechanism of superconductivity for partially occupied electrons in the p and d orbitals is proposed in two component spinless fermion system with different band widths. The ground state energy and the partition function are calculated in generalized mean field approximation by introducing diagonal charge-order parameter and off-diagonal superconducting order parameter. The self-consistent system of equations are analyzed and the phase diagram in the ground state and at finite temperatures are obtained for arbitrary bandwidths and different concentration of particles.

[J11.08] Low Energy Model Hamiltonians for High T_c Cuprates.

The recently developed TB-LMTO-ASA downfolding technique is employed to obtain orthogonal, two-centered, nearest neighbor tight-binding model Hamiltonians for the CuO planes for several High T_c cuprates. We show that our model is generic and is capable of reproducing the non-trivial details of the low energy LDA band structure, in particularly those arising from the dimpling of the CuO planes and variation of the apical oxygen distance to plane Cu. We use this model to compute the electron-phonon interaction for the buckling mode with dimpled CuO planes and discuss its consequences for d-wave superconductivity.

[J11.09] Pressure behaviour of the electric-field gradients in \bfYBa_2Cu_4O_8

An unusual behaviour of the electric field gradients (EFG's) at Cu nuclear sites for YBa_2Cu_4O_8 (Y124) under pressure have been obtained within the Local Density Approximation (LDA) using the FP-LAPW method. The importance of the inclusion of localized orbitals to deal with errors due to extended core states or linearization of narrow states is demonstrated by comparing to results obtained by an FP-LMTO implementaion which uses a more standard two panel scheme to deal with semicore states. The calculated EFG's at ambient pressure agree with theoretical values which exist in the literature for plane and chain Cu and oxygens but give quite different results for Y and Ba. Similar to what occurs in YBa_2Cu_3O_7 the EFG's for which there exist experimental determinations are reproduced except plane-Cu, but in Y124 a factor 3 discrepancy is found. The smaller predicted anisotropy has been attributed to a real failure of LDA. As pressure is increased the EFG's at Cu sites remain practically constant. A detailed analysis is made of the origin of the EFG and how it depends on pressure. Since many properties of Y124, including T_c, are very sensitive to pressure we propose that experiments under pressure could be used to examine further the validity of predictions based of LDA calculations for H-T_c materials.

[J11.10] Crystal-field effects in Ln_2-zCe_zCuO_4 homologues

Ln_2-zCe_zCuO_4 (Ln214) superconduct for Ln=Pr, Nd, Sm, and Eu, but not for trivalent Gd^+3 or for rare-earth ions smaller than Gd^+3, or for Cm^+3 (with Th replacing Ce). This is not exclusively a size effect, because Cm^+3 has a size between those of Pr^+3 and Nd^+3, and both Pr214 and Nd214 superconduct, but Cm214 does not. [H. A. Blackstead and J. D. Dow, Phys. Lett., in press.] The important question to ask is ``Why can any of the Ln214 homologues superconduct when Ln is magnetic and adjacent to the superconducting condensate?'' The answer is that crystal-field splitting inhibits pair-breaking by the magnetic rare-earth ion: the magnetic L=0 trivalent ions Gd and Cm do not experience crystal-field splitting, and so break Cooper pairs and destroy superconductivity in Gd_2-zCe_zCuO_4 and Cm_2-zTh_zCuO_4. The remaining Ln214 materials that do superconduct with magnetic Ln all experience crystal-field splitting and also exhibit a size-effect that is related to oxygen doping.

[J11.11] Symmetry of the Gap Parameter and Evaluation of T_c in the Framework of the Dipolon Theory for the High Temperature Superconductor Bi_2Sr_2CaCu_2O_8.

This abstract was not submitted electronically.

[J11.12] Quantum Nucleation of Soliton-Antisoliton Pairs in a Dissipative \phi^4 Field Theory in 1 + 1 Dimensions.

The rate at which solitons are created is calculated for a one dimensional \phi^4 field theory, in which the effect of a coupling to a heat bath is also included. The coupling of the field to the heat bath produces a mechanism in which thermal equilibration can be established via transfer of energy between the field and it's environment. In this field theory solitons and anti-solitons are created in pairs, due to topological considerations. The soliton nucleation rate is calculated using the Instanton Method, as modified by incorporation of finite temperatures. Our results go beyond the thin wall approximation that has been previously used. We find that at sufficiently low temperatures, the solitons are produced by quantum tunneling and that the dissipation suppresses the nucleation rate, and at high temperatures the rate is governed by thermally activation of a critical bubble. In this high temperature regime, the thermal activation energy is independent of the strength of the dissipative coupling. Our results show a smooth cross-over, between the low temperature quantum nucleation regime and the high temperature thermally activation regime, which occrs at a characteristic temperature T_c. We also examine and discuss the possible physical significance of the existence of a second characteristic temperature, T_0, within the quantum nucleation regime, at which the thin wall approximation breaks down.

[J11.13] Anisotropic s or d- wave pairing in the Hubbard model

The pairing instability in the Hubbard and the extended Hubbard models for a 2D lattice is examined by using the perturbation diagram approach. A graphical technique based on Ward's identity is used to represent the two-particle interactions in both singlet and triplet channels. The kernel of two-particle interactions in the spin and charge channels and the irreducible spin and charge density response functions are also considered. The t-matrix approach is used to investigate the pairing instability induced by the particle-hole excitations including both the Coulomb and the electron-paramagnon interactions. The expansion of the equation for the t-matrix over the Legendre polynomials is used to find the singularity in harmonics of the t-matrix equation for different l, the orbital momentum. It is found that the pairing instability in the singlet channel can happen either in the state with l=0 (s-wave) or in the state with l=2 (d-wave). T_c for both s- and d-wave states is calculated by using the pole condition of the t-matrix. An anisotropic s-wave state near the SDW instability resembles the d_x^2-y^2 wave symmetry as shown, but without the sign changes in the gap function.

Part J of program listing