Dr. Jürgen Stein

Abstracts

J. Stein, N. Sahoo, S. B. Sulaiman, T. P. Das: Theory of Cu-63 nuclear quadrupole interaction in cuprite, Hyperfine Interact. 60 (1990) 849

The nuclear quadrupole interaction of Cu-63 in Cu₂O has been studied by the first-principles Hartree-Fock cluster procedure. The influence of the ions outside the cluster has been incorporated explicitly in the Hamiltonian. The results are compared with results from experiment, ionic models, and other approaches.

S. B. Sulaiman, N. Sahoo, S. Markert, J. Stein, T. P. Das, K. Nagamine: Theory of electron distributions and Cu-63 and O-17 nuclear quadrupole interactions in YBa₂Cu₃O₇ and YBa₂Cu₃O₆, Bull. Mater. Sci. 14 (1991) 149

Ab initio unrestricted Hartree-Fock cluster investigations have been carried out on the electronic structures of the YBa₂Cu₃O₇ and YBa₂Cu₃O₆ systems. The results of these investigations provide satisfactory explanations of available Cu-63 and O-17 nuclear quadrupole interaction data. The electron distributions obtained rule out the presence of Cu+3 ions and are supportive of the presence of Cu+2, Cu+1, O-1 ions in the O₇ system and Cu+2, Cu+1, O-2 in the O₆ system with actual charges departing significantly from the formal charges, especially in the O₇ system, indicating the possible sources that can bridge the remaining gap between theoretical and experimental results for the nuclear quadrupole interaction parameters.

J. Stein, R. Oppermann: A spin-dependent Popov-Fedotov trick and a new loop expansion for the strong-coupling negative-U Hubbard model, Z. Phys. B 83 (1991) 333

We calculate fluctuation effects on Bose-condensation-type superconductivity in the strong-coupling negative-U Hubbard model by means of a new loop expansion. Our method is based on a spin-dependent modification of the Popov-Fedotov trick. We replace the Popov-Fedotov chemical potential by a fictitious imaginary magnetic field. This field is absorbed in spin-dependent semionic Matsubara frequencies, which allows for a mixed-statistics representation of the anisotropic quantum spin-1/2 Heisenberg model. We report results at one-loop order for the superconducting order parameter, for the critical temperature, for the chemical potential, and for the excitation spectra both above and below T_c. We identify mean-field results in zeroth loop order and we find both dimensional and filling (n-)depending singularities in interaction fluctuations at one-loop order. Renormalization of dimensional singularities is carried out in four dimensions. Divergencies with n(1-n) -> 0 in the dilute limits indicate the breakdown of mean-field solutions, but superconductivity persists for arbitrarily small n(1-n), if our loop expansion is interpreted by exponential behaviour as it is suggested by the abelian nonlinear sigma-model.

J. Stein, R. Oppermann: -pairing superconductivity in the spin-polarized strong-coupling negative-U Hubbard model, Phys. Rev. B 46 (1992) 8409

We have calculated the effect of a single unpaired electron on superconductivity in the strong coupling negative-U Hubbard model, employing a diagram technique with generalized Matsubara frequencies. Using a generalization of the Hamiltonian to n orbitals per site and applying a geometry-controlled approximation in the limit of high coordination numbers z, we perform a loop expansion of the model. This allows to incorporate fluctuation corrections to the mean field solution which emerges as result in lowest order of the loop expansion. We show that in the limit U -> infinity the mean field solution exhibits a phase transition to an antiferrosuperconducting state which is characterized by a "staggered" local superconducting order parameter with its sign alternating from site to site. This superconducting state (referred to as "-pairing" state by a number of authors) for the attractive case is related to the Nagaoka ground state of the repulsive Hubbard model by a partial particle-hole transformation. We have found that the model in the slightly spin-polarized case (i.e. when a single unpaired electron is present) for highly coordinated lattices and in lowest loop order is equivalent to a pair hopping model with temperature dependent repulsive coupling. In this paper we report the mean field results for the transition temperature, the order parameter, the chemical potential, the upper critical magnetic field H_c2 and excitation spectra both above and below T_c and demonstrate that the system exhibits a complete Meissner effect.

J. Stein: Field theoretic treatment of the strong-coupling attractive Hubbard model with diagonal disorder, J. Phys. Condens. Matter 5 (1993) 371

We present a field theoretic formulation of the strong-coupling attractive Hubbard model with Gaussian distributed random on-site energies. Selfconsistency equations for the order parameters of superconductivity and charge ordering are derived at lowest loop order and solved for the limiting cases of weak and strong disorder. We also study dynamical properties and calculate the influence of disorder on the Bogoliubov-Anderson mode in the superconducting phase.

J. Stein: -pairing superconductivity in the negative-U Hubbard model: Effect of fluctuations and disorder, Int. J. Mod. Phys. B 8 (1994) 2041

We have studied the influence of singular fluctuations around the mean field solution as well as higher order contributions to the geometry-controlled asymptotic expansion of the propagators on -pairing superconductivity in the strong coupling negative-U Hubbard model in the presence of unpaired electrons. The modifications of the mean field results due to introduction of disorder and allowance for finite U are also calculated. Besides the singularities already present in the O(2) nonlinear sigma-model we find a filling depending singular depression of the repulsive effective pair hopping interaction which strongly alters the mean-field phase diagram and appears to suppress the -pairing phase near the band edges.

J. Stein, R. Oppermann: One-loop result for the Bogoliubov-Anderson mode of the superconducting strong-coupling attractive Hubbard model, Phys. Lett. A 184 (1994) 370

We present the one-loop calculations for the sound-like Bogoliubov-Anderson mode in the superconducting phase of the attractive Hubbard model in the strong-coupling limit. It is found that in the leading dimensional singularities and for low temperatures the zero-loop expression is modified only by a global correction factor; as a consequence, the dispersion relation and the Bogoliubov velocity retain their zero-loop results.

O. Veits, R. Oppermann, M. Binderberger, J. Stein: Extension of the Popov-Fedotov method to arbitrary spin, J. Phys. I France 4 (1994) 493

The partition function and thermodynamic expectation values of a spin system with arbitrary spin quantum number are expressed by an exact fermionic representation on Fock space. Extending a suggestion of Popov and Fedotov, this is achieved by introducing a set of imaginary chemical potentials. Spin operators are replaced by usual bilinear combinations of Fermi operators satisfying the spin commutation relations.

J. Stein: Coupling of fluctuation modes in the disordered strongly attractive Hubbard model, Z. Phys. B 95 (1994) 79

The coupling of two different types of soft modes related to interaction-generated superconducting and disorder-generated (pseudo)diffusive fluctuations in the large negative-U Hubbard model with random local energies is studied in the framework of a Grassmann field theoretic approach with modified semionic Matsubara frequencies. In leading loop order it is found that the sound-like order parameter phase fluctuation mode retains its massless nature with only its velocity being modified, as expected from the generalized Ward identity. The disorder-induced fluctuations which are originally completely local due to the locality of disorder correlations acquire true diffusive behaviour by interaction effects in the superconducting phase.

J. Stein, O. Entin-Wohlman, A. Aharony: Weak ferromagnetism in the low-temperature tetragonal phase of the cuprates, Phys. Rev. B 53 (1996) 775 (Postscript-File)

The criterion for the existence of weak ferromagnetism in the low-temperature distorted phases of La₂CuO₄-type compounds is derived on the basis of a general superexchange Hamiltonian. It is found that a ferromagnetic canting out of the CuO₂ planes is excluded in the pure low-temperature tetragonal phase. The anisotropic superexchange interactions between the copper spins are obtained from a Hubbard model which includes all copper 3d and oxygen 2p orbitals, and all on-site Coulomb matrix elements. The results apply when the oxygen octahedra surrounding each copper have tetragonal symmetry. Explicit expressions for the net ferromagnetic moment and the in-plane and the out-of-plane gaps in the spin-wave spectrum are derived and estimated in terms of the microscopic parameters of the cuprates.

J. Stein: Nonlocal Coulomb interactions and the magnetic anisotropies in the low-temperature phases of the cuprates, Phys. Rev. B 53 (1996) 785 (Postscript-File)

We have extended and generalized earlier studies of the magnetic anisotropies of the Cu spins in the copper-oxide planes generated by the spin-orbit coupling on the coppers and by the nonlocal Coulomb interactions between neighboring ions. Our derivation of the anisotropic magnetic Hamiltonian includes the contributions from general matrix elements of the Coulomb interaction both between the copper ions of a single bond and between the adjacent copper and oxygen sites. The results apply for a general rotation axis of the oxygen octahedra, with the assumption of tetragonal site symmetry of the copper. This mechanism leads to a form of the anisotropic spin interaction between the Cu ions which is identical to the one generated by kinetic superexchange in the presence of purely local Coulomb interactions. Together with the numerical estimates for the resulting spin couplings, this indicates that the Coulomb direct exchange leads to significant contributions to the isotropic spin interaction and the out-of-plane anisotropy, but does not affect qualitatively the magnetic order in the ground state.

J. Stein: Critical properties of a spin glass with anisotropic Dzyaloshinskii-Moriya interaction, J. Phys. A 29 (1996) 963 (Postscript-File)

We study the classical n-vector spin glass with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. A random DM interaction with m independent and separated couplings defines a generalized gauge glass model with a O(n-2m) X^m O(2) rotational symmetry and a broken global reflection invariance. It is shown that this model is in the same universality class as the random gauge XY ("gauge glass") model. With an additional uniaxial anisotropy, a crossover from Ising-like to gauge glass critical behaviour is found for a sufficiently large variance of the DM interaction. A new situation arises when there is correlation between the separated random DM couplings. We show that the critical behaviour of a spin glass with two correlated couplings of the anisotropic DM interaction is in a new universality class. The critical exponents eta and nu of this model are calculated at two-loop order near six dimensions. We also present a simplified and more rigorous field theoretic analysis of the gauge glass model.

J. Stein: Critical exponents of the U(n) vector spin glasses, Europhys. Lett. 34 (1996) 717 (Postscript-File)

The critical exponents of the classical spin glasses with symmetry are obtained to order of the -expansion around six dimensions, where . This new unitary symmetry is realized in the m-vector () spin glasses with anisotropic quenched random Dzyaloshinskii-Moriya (DM) interaction. Such a random DM interaction with n correlated couplings leads to critical exponents which are different from those of any isotropic m-vector spin glass and thus belong to new universality classes.

J. Stein: Interacting fluctuations and the two-loop order parameters of the strong-coupling negative-U Hubbard model, Nucl. Phys. B 483 (1997) 552 (Postscript-File)

The effective field theory that describes the interaction of fluctuations of the attractive Hubbard model in the strong-coupling limit is formulated and applied to obtain the two-loop results for the order parameters of the model at low temperatures and in the leading singularities near two dimensions. Starting from a Grassmann functional integral representation of the strong-coupling model on the restricted fermionic Hilbert space, which corresponds to the anisotropic spin-1/2 Heisenberg quantum antiferromagnet, we derive the effective field theory up to fifth order in the bosonic fluctuation fields. The loop-corrections of the order parameters for superconductivity and charge-ordering and of the chemical potential are evaluated including both the singular planar phase fluctuations and the out-of-plane fluctuations, which become soft at half band-filling. The results are in agreement with the scaling behaviour expected from the corresponding XY and Heisenberg limits of the O(n) nonlinear sigma-model.

J. Stein: Superfluid density of the two-dimensional strong-coupling attractive Hubbard model, Phys. Lett. A 224 (1997) 282 (Postscript-File)

The low-temperature result for the superfluid density of the attractive (negative-U) Hubbard model in two dimensions and in the strong-coupling limit is obtained, applying a field-theoretic representation of the model and utilizing a hydrodynamic relation between the order parameter field, the correlation function for soft planar fluctuations, and the superfluid density. This microscopic derivation does not involve self-consistency arguments and allows to include the influence of the out-of-plane pseudo-spin fluctuations which become singular at half band-filling and suppress a Kosterlitz-Thouless transition at finite temperature. The result is in good agreement with quantum Monte Carlo data.

J. Stein: Flow equations and the strong-coupling expansion for the Hubbard model, J. Stat. Phys. 88 (1997) 487 (Postscript-File)

Applying the method of continuous unitary transformations to a class of Hubbard models, the derivation of the t/U-expansion for the strong-coupling case is re-examined. The flow equations for the coupling parameters of the higher-order effective interactions can be solved exactly, resulting in a systematic expansion of the Hamiltonian in powers of t/U, valid for any lattice in arbitrary dimension and for general band-filling. The expansion ensures a correct treatment of the operator products generated by the transformation, and only involves the explicit recursive calculation of numerical coefficients. This scheme provides a unifying framework to study the strong-coupling expansion for the Hubbard model, which clarifies and circumvents several difficulties inherent to earlier approaches. Our results are compared with those of other methods, and it is shown that the freedom in the choice of the unitary transformation that eliminates interactions between different Hubbard bands can affect the effective Hamiltonian only at order t^3/U^2 or higher.

J. Stein: Quantum fluctuations and the ground-state phase diagram of the strong-coupling Holstein-Hubbard model, Europhys. Lett. 39 (1997) 413 (Postscript-File)

A Grassmann functional integration technique is applied to the anisotropic pseudospin Hamiltonian derived from the Holstein-Hubbard model with strong electron-phonon coupling. It is found that in those regions of the low-temperature phase diagram where superconductivity and the charge-density wave coexist already the static and homogeneous saddle-point solution of the resulting field theory yields a ground-state energy which is lower than the classical result corresponding to the usual mean-field solution. This is due to the presence of quantum fluctuations and leads to new ground-state phase boundaries quantitatively different from those obtained in previous work by conventional operator decoupling schemes.

J. Stein: Flow equations and extended Bogoliubov transformation for the Heisenberg antiferromagnet near the classical limit, Eur. Phys. J. B 5 (1998) 193 (Postscript-File)

The Heisenberg spin-S quantum antiferromagnet is studied near the large-spin limit, applying a new continuous unitary transformation which extends the usual Bogoliubov transformation to higher order in the 1/S-expansion of the Hamiltonian. This allows to diagonalize the bosonic Hamiltonian resulting from the Holstein-Primakoff representation beyond the conventional spin-wave approximation. The zero-temperature flow equations derived from the extension of the Bogoliubov transformation to order 1/S^2 for the ground-state energy, the spin-wave velocity, and the staggered magnetization are solved exactly and yield results which are in agreement with those obtained by a perturbative treatment of the magnon interactions.

J. Stein: Flow equations and the Ruderman-Kittel-Kasuya-Yosida interaction, Eur. Phys. J. B 12 (1999) 5 (Postscript-File)

The method of continuous unitary transformations is applied to obtain the indirect exchange coupling between local magnetic moments in an electron gas. The derivation of the exact analytical expression for the resulting Ruderman-Kittel-Kasuya-Yosida interaction is presented for general dimensionality. In odd dimensions, the result can be shown explicitly to exhibit universal 2k_F oscillatory behaviour on all length scales.

J. Stein: Unitary flow of the bosonized large-N Lipkin model, J. Phys. G 26 (2000) 377 (Postscript-File)

The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N. The transformed Hamiltonian is diagonal in order 1/N^3, extending known linear transformations to next-higher orders in the inverse particle number. This approach quite naturally allows to preserve the tridiagonal structure of the original Lipkin Hamiltonian in the course of the transformation. Exact analytical results for the coupling functions and explicit expressions for the ground-state energy and for the energy gap to the first excited state in order 1/N^2 are presented and are compared with the accurate numerical values.

J. Stein: Flow equations and new weak-coupling solution for the spin-polaron in a quantum antiferromagnet, Europhys. Lett. 50 (2000) 68 (Postscript-File)

The t-J model for the doped two-dimensional Heisenberg quantum antiferromagnet is studied in the generalized Dyson-Maleev representation, applying a new continuous unitary transformation which eliminates the coupling of spin and charge degrees of freedom. The analytical solutions of the resulting flow equations are derived in the weak-coupling regime where t/J is small. This continuous transformation yields a new weak-coupling result for the dispersion of the spin-polaron, if the elimination of both the nondiagonal spin-wave contributions and the terms coupling holes and spin-waves is performed simultaneously. The associated one-particle ground state is lower in energy than the corresponding perturbative result, which is reproduced upon application of subsequent transformations.