A theoretical analysis of the magnetic properties of La<Subscript>2</Subscript>CuO<Subscript>4</Subscript>

The magnetic properties of the La₂CuO₄ are analyzed by means of the paramagnetic solution of the Hubbard model within the composite operator method. The experimental findings of the inelastic neutron magnetic scattering [R. Coldea et al., Phys. Rev. Lett. 86, 5377 (2001)] for the spin spectrum, the spin-wave intensity and the behavior of the dispersion at the zone boundary are well described by our results although the difference in phase. The Hubbard model emerges has a minimal model capable to describe the anomalous magnetic behavior of such a strongly correlated material. Received 29 July 2002 / Received in final form 2 January 2003 Published online 14 March 2003     

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction U_c remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Spin-wave theory for finite classical magnets and superparamagnetic relation

Analytical calculations based on finite-size spin-wave theory and Monte Carlo (MC) simulations are performed to investigate the validity of the well-known relation m(H, T) = M(H, T)B _D[M(H, T) H/T] between the induced magnetization m of the magnetic particle and its intrinsic magnetization M for the Ising and isotropic classical models (B _D(x) is the Langevin function, D is the number of spin components, is the number of atoms in the particle). It follows from general arguments and from our analytical results for the Heisenberg model at T≪T _c that this relation is not exact for any finite D and nonzero temperature. Nevertheless, corrections to this formula remain very small practically in the whole range T < T _c if ≫ 1, as confirmed by our Monte Carlo calculations. At T T _c/4 there is a good agreement between the MC and finite-size spin-wave calculations for the field dependence of m and M for the Heisenberg model with free boundary conditions. Received 1st December 2000     

Effects of antisymmetric interactions in molecular iron rings

The level crossing mechanism between the ground and the first excited state of Na:Fe₆ antiferromagnetically coupled iron rings is studied by torque magnetometry down to 40 mK and in magnetic fields up to 28 T. The step width at the crossing field B_c assumes a finite value at the lowest temperatures. This fact is ascribed to the presence of level anticrossing, not expected for a ring with axial, i.e. S₆ point group, symmetry. Assuming a reduced symmetry, we revised the model Hamiltonian of such a spin system by introducing a Dzyaloshinsky-Moriya (DM) term and we show, by exact diagonalization, that DM term can account for the mixing of states with different parity. In particular, analytical as well numerical analysis show that the introduction of the DM term may contribute to the broadening of the torque step as well as for the finite energy gap at B_c observed by heat capacity in a similar ring Li:Fe₆ as previously reported [#!aclbg!#]. Received 3 September 2002 Published online 31 December 2002     

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k _F charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological solitons carrying charge e/2 and spin zero. Relevance to the 4k _F charge density wave instability in (DI - DCNQI)₂ A g or recently discovered in (TMTTF)₂X ( X=PF ₆, AsF₆) is discussed. Received 30 March 2001 and Received in final form 11 May 2001     

The glassy phase of Gallager codes

Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q _EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes. Received 9 April 2001     

Solitons in the spin-Peierls compound CuGeO <Subscript>3</Subscript>

We calculate the excitation gap, the soliton energy, and the soliton density at finite temperature, of the spin-1/2 one dimensional antiferromagnet coupled to phonons, using a self-consistent harmonic approximation, and the thermal-Green function technique. The spin degrees of freedom are represented by the phase Hamiltonian with the help of the boson representation of the spinless fermions. We estimate the critical field H_c above which begins the incommensurate phase. We also present a theoretical calculation for the specific heat in this phase. We use CuGeO₃ as an example of a compound where our theory could be applied. Received 22 October 2002 / Received in final form 21 January 2003 Published online 14 March 2003     

Magnetic properties of undoped YBa 2 Cu 3 O 6 + x system

In the present paper, we study the magnetic properties of bilayer cuprate antiferromagnets. In order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, Néel temperature and the magnetic contribution to the specific heat, the double time Green's function technique has been employed in the random phase approximation (RPA). The spin wave dispersion curve for a bilayer antiferromagnetic system is found to consist of one acoustic and one optic branch. The “optical magnon gap” has been attributed solely to the intra-bilayer exchange coupling (J _⊥ ) as its magnitude does not change significantly with the inter-bilayer exchange coupling (J_z). However J_z is essential to obtain the acoustic mode contribution to the magnetization. The numerical calculations show that the Néel temperature (T _N ) of the bilayer antiferromagnetic system increases with the J_z and a small change in J_z gives rise to a large change in the Néel temperature of the system. The magnetic specific heat of the system follows a T² behaviour but in the presence of J_z it varies faster than T². Received 13 July 2000 and Received in final form 14 May 2001     

Critical behaviour near the metal-insulator transition of a doped Mott insulator

We have studied the critical behaviour of a doped Mott insulator near the metal-insulator transition for the infinite-dimensional Hubbard model using a linearized form of dynamical mean-field theory. The discontinuity in the chemical potential in the change from hole to electron doping, for U larger than a critical value U _c, has been calculated analytically and is found to be in good agreement with the results of numerical methods. We have also derived analytic expressions for the compressibility, the quasiparticle weight, the double occupancy and the local spin susceptibility near half-filling as functions of the on-site Coulomb interaction and the doping. Received 15 March 2001 and Received in final form 22 May 2001     

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces. Received 11 April 2001 and Received in final form 6 September 2001     

Understanding the proton spin “puzzle” with a new “minimal” quark model

We investigate the spin structure of the nucleon in an extended Jaffe-Lipkin quark model. In addition to the conventional 3q structure, different (3q)(Q ) admixtures in the nucleon wave function are also taken into account. The contributions to the nucleon spin from various components of the nucleon wave function are discussed. The effect due to the Melosh-Wigner rotation is also studied. It is shown that the Jaffe-Lipkin term is only important when antiquarks are negatively polarized. We arrive at a new “minimal” quark model, which is close to the naive quark model, in order to understand the proton spin “puzzle”. Received: 4 November 2000 / Accepted: 23 October 2001     

Magnetic excitations in charge ordered a' - {N_a}{V_2}{O_5}

An investigation of the spin excitation spectrum of charge ordered (CO) NaV₂O₅ is presented. We discuss several different exchange models which may be relevant for this compound, namely in-line and zig-zag chain models with weak as well as strong inter-chain coupling and also a ladder model and a CO/MV (mixed valent) model. We put special emphasis on the importance of large additional exchange across the diagonals of V-ladders and the presence of exchange anisotropies on the excitation spectrum. It is shown that the observed splitting of transverse dispersion branches may both be interpreted as anisotropy effect as well as acoustic-optic mode splitting in the weakly coupled chain models. In addition we calculate the field dependence of excitation modes in these models. Furthermore we show that for strong inter-chain coupling, as suggested by recent LDA + U results, an additional high energy optical excitation appears and the spin gap is determined by anisotropies. The most promising CO/MV model predicts a spin wave dispersion perpendicular to the chains which agrees very well with recent results obtained by inelastic neutron scattering. Received 30 April 1999 and Received in final form 5 October 1999     

Stripe orders driven by long-range Coulomb forces in the 2D-Hubbard model

Within the single band 2D-Hubbard model treated by means of a strong-coupling approach based on a cumulant expansion and a nonstandard diagrammatic technique, we discuss the existence of critical charge fluctuations that could give rise to an instability towards a phase separation (PS). It turns out that such instability exists and evolves into an incommensurate charge density wave (ICDW) when long-range Coulomb forces are taken into account. We find a stripe phase with a crossover from diagonal to vertical stripes at increasing doping in the range 0.01 ?δ? 0.2 and increasing Coulomb potential U, similarly to recent NMR experiments on La _{2 - x} Sr _x CuO ₄. Received 20 November 2000     

Exact diagonalization of the S = 1/2 XY ferromagnet on finite bcc lattices to estimate T = 0 properties on the infinite lattice

In this paper finite bcc lattices are defined by a triple of vectors in two different ways - upper triangular lattice form and compact form. In Appendix A are lists of some 260 distinct and useful bcc lattices of 9 to 32 vertices. The energy and magnetization of the S = 1/2 XY ferromagnet have been computed on these bcc lattices in the lowest states for S _z = 0, 1/2, 1 and 3/2. These data are studied statistically to fit the first three terms of the appropriate finite lattice scaling equations. Our estimates of the T = 0 energy and magnetization agree very well with spin wave and series expansion estimates. Received 1st August 2000 and Received in final form 22 December 2000     

Derivation of effective spin models from a three band model for CuO-planes

The derivation of effective spin models describing the low energy magnetic properties of undoped CuO₂-planes is reinvestigated. Our study aims at a quantitative determination of the parameters of effective spin models from those of a multi-band model and is supposed to be relevant to the analysis of recent improved experimental data on the spin wave spectrum of La₂CuO₄. Starting from a conventional three-band model we determine the exchange couplings for the nearest and next-nearest neighbor Heisenberg exchange as well as for 4- and 6-spin exchange terms via a direct perturbation expansion up to 12th (14th for the 4-spin term) order with respect to the copper-oxygen hopping t_pd. Our results demonstrate that this perturbation expansion does not converge for hopping parameters of the relevant size. Well behaved extrapolations of the couplings are derived, however, in terms of Padé approximants. In order to check the significance of these results from the direct perturbation expansion we employ the Zhang-Rice reformulation of the three band model in terms of hybridizing oxygen Wannier orbitals centered at copper ion sites. In the Wannier notation the perturbation expansion is reorganized by an exact treatment of the strong site-diagonal hybridization. The perturbation expansion with respect to the weak intersite hybridizations is calculated up to 4th order for the Heisenberg coupling and up to 6th order for the 4-spin coupling. It shows excellent convergence and the results are in agreement with the Padé approximants of the direct expansion. The relevance of the 4-spin coupling as the leading correction to the nearest neighbor Heisenberg model is emphasized. Received 8 June 2001 / Received in final form 28 May 2002 Published online 19 July 2002     

Generic replica symmetric field-theory for short range Ising spin glasses

Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations. Received 9 October 2001     

Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, J _bb/J _bv. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S _tot = 0 and 1, but not for S _tot = 2, and has a gap only in the interval 0.4874(1) ⩽ J _bb/J _bv ⩽ 1.53(1). The gap, known to be dispersionless for J _bb = J _bv, is found to acquire increasing k-dependence as J _bb/J _bv moves away from unity. Received 29 October 2002 / Received in final form 14 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: sblundell@cea.fr RID="b" ID="b"e-mail: nunezreg@lps.u-psud.fr