M. Deeg

Electron correlations and quantum lattice vibrations in strongly coupled electron-phonon systems: a variational slave boson approach

We investigate the ground-state properties of the two-dimensional Hubbard model with an additional Holstein-type electron-phonon coupling on a square lattice. The effects of quantum lattice vibrations on the strongly correlated electronic system are treated by means of a variational squeezed-polaron wave function proposed by Zheng, where the possibility of static (frozen) phonon-staggered ordering is taken into account. Adapting the Kotliar-Ruckenstein slave boson approach to the effective electronic Hamiltonian, which is obtained in the vacuum state of the transformed phonon subsystem, our theory is evaluated within a two-sublattice saddle-point approximation at arbitrary band-filling over a wide range of electron-electron and electron-phonon interaction strengths. We determine the order parameters for long-range charge and/or spin ordered states from the self-consistency conditions for the auxilary boson fields, including an optimization procedure with respect to the variational displacement, polaron and squeezing parameters. In order to characterize the crossover from the adiabatic (ω=0) to the nonadiabatic (ω=∞) regime, the frequency dependencies of these quantities are studied in detail. In the predominant charge (spin) ordered phases the static Peierls dimerization (magnetic order) is strongly reduced with increasing ω. As the central result we present the slave boson ground-state phase diagram of the Holstein-Hubbard model for finite phonon frequencies.

Slave boson mean field theory for the 2-D Peierls-Hubbard system

Adapting the Kotliar-Ruckenstein slave boson approach to the Hubbard model with an additional local electronphonon interaction, we have studied the stability of the ground state against (π, π) and (π, 0) Peierls distortions on a square lattice. The theory is evaluated within an adiabatic two-sublattice saddle-point approximation restricted to symmetry broken states compatible with the underlying bipartite lattice, i.e. para-, ferro-, ferri- and antiferromagnetic states with and without static lattice displacement. At half-filling the Holstein coupling leads to a stable paramagnetic phase with an on-site frozen in breathing mode accompanied by a long-range charge density wave below a critical Hubbard interactionU. Away from half-filling, we distinguish between two possible phase diagrams of the Peierls-Hubbard model. One of them is obtained in the usual way of comparing the relative stability of several homogeneous phases, the other more complete one allows for heterogeneous mixing of phases. In this case we found phase separated regions with an without ‘dimerization’, homogeneous ‘dimerized’ para- and ferrimagnetic states, and the pure para-and ferromagnetic phases. Upon doping the local electron-phonon coupling can induce a magnetic ordered state.

Magnetic Phase Diagram and Transport Properties of the t-J Model: A Spin-Rotation-Invariant Slave-Boson Approach

On the basis of a spin-rotation-invariant formulation of the Kotliar-Ruckenstein slave-boson representation the t-J model is studied on a square lattice. The ground-state phase diagram is derived numerically, by taking into account also incommensurate magnetic structures. The domain of phase separation is determined. The correlation-induced band renormalization is in excellent agreement with Lanczos results. We calculated the doping dependence of Hall resistivity and thermopower using the relaxation time approximation, the results being in accord with experiments on La2-?Sr?CuO4.

Hall resistivity of hole- and electron-doped high-Tc cuprates

Abstract We investigate the doping dependence of the Hall resistivity of high-Tc superconductors in terms of the t-t′-J model using a spin-rotation-invariant slave-boson technique. A second-neighbour hopping t′ of different sign is included in order to reproduce the Fermi surfaces of both hole- and electron-doped systems in the noninteracting limit. Correlation effects are responsible for renormalization of the quasiparticle band. The results of our slave-boson calculation are in excellent agreement with experiments on La2−xSrxCuO4, YBa2Cu3O6+x, and Nd2−xCexCuO4.

Dynamic spin and charge susceptibilities in thet−J model

Based on the spin-rotation-invariant formulation of the Kotliar Ruckenstein slave-boson representation, the paramagnetic spin and charge susceptibilities in thet-J model are calculated. Analyzing the static spin susceptibility, the instability of the paraphase towards incommensurate magnetic order is in agreement, with the saddle-point phase diagram recently obtained by some of the authors. The spin dynamics at arbitrary frequencies, wave vectors and band fillings is calculated, where the Fermi-surface and correlation effects are studied. The magnetic instability region is investigated with respect to the formation of a collective spin-fluctuation mode. Near the transition point, a kinetic gap and a sharp peak in the spectral weight ((1,0) paramagnon) are obtained.

Slave-boson phase diagram of the two-dimensional extended Hubbard model: Influence of electron-phonon coupling

We present a detailed study of the extended Hubbard-Peierls model on a square lattice using the slave-boson method proposed by Kotliar and Ruckenstein. The emphasis is on the investigation of the ground state phase diagram. To compare the relative stability of several homogenous phases, the effective bosonized action was evaluated by means of a two-sublattice saddlepoint approximation which allows for the symmetry broken states compatible with the underlying bipartite lattice structure. Paying particular attention to the interplay of electron-electron and electron-phonon interaction, we take into account various types of magnetic ordered phases, i.e. para-, ferro-, ferri-, and antiferromagnetic states, as well as charge ordered phases, e.g. a static (π, π) Peierls distorted state. Furthermore the approach has been applied to the following special cases: the Hubbard model, the extended Hubbard model, and the Hubbard-Peierls model. A careful numerical solution of the corresponding self-consistency equations enables us to map out the ground-state phase diagrams of the various models at arbitrary band filling over the whole range of interaction strength. In the phase diagram of the Hubbard model we found a large region with ferrimagnetic order away from half-filling. The phase diagram of the halffilled band extended Hubbard model shows a first-order transition from a spin-density-wave to a charge-density-wave state which is displaced from the mean-field lineU=4V towards largerV. At large negativeU andV we obtain a domain with charge separation. The phase compares favorably with earlier quantum Monte-Carlo results. Including the local electron-phonon coupling the charge-density-wave region is considerably enlarged. Away from half-filling the phase diagram becomes more complex: besides the pure magnetic phases we obtain ferri- and paramagnetic states which show additional charge-density order. Aspects of phase separation are discussed. Finally we investigate the variation of the different gap and order parameters along characteristic lines in the parameter space and determine the renormalized quasiparticle bands.

Transport and charge/magnetic order in the 2D Holstein/t-t′-J model

Abstract The magnetic phase diagram of the t-t′-J model is presented, where in the framework of a spin-rotation-invariant slave-boson approach incommensurate magnetic structures are taken into account. Including Gaussian fluctuations, a general expression for the dynamic spin and charge susceptibilities of the t-t′-J model is derived, which goes beyond RPA. The doping dependence of the Hall resistivity is calculated, the results being in accord with experiments on LSCO and YBCO. The commensurate charge/lattice modulations, reported recently for the isostructural nickelates at quarter filling, can be understood in terms of the 2D Holstein-t-J model.

A Variational Slave Boson Approach to the Holstein-Hubbard Model

Research on the high-T c cuprates has focused, once again, interest on strongly coupled electron-phonon (EP) systems. Although it is widely believed that most of the unusual normal-state properties of these materials may be related to strong electronic correlations, many experiments have indicated also a substantial EP coupling. Especially the importance of polaron formation in the cuprate superconductors is a heavily debated issue.1 Motivated by this situation the aim of our contribution is to analyze the main features of the ground-state phase diagram of a simple microscopic EP model, by means of a variational slave boson (SB) approach.2, 3 This technique facilitates a unique treatment of electron-electron and EP interaction,4, 5 and allows an interpolation between weak and strong coupling regimes as well as between adiabatic and antiadiabatic limits.