Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians

In the first part of this paper, the extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. A counter example to the original formulation of Lieb-Schultz-Mattis and Affleck is exhibited and a more precise statement is formulated. The degeneracy of the ground-state in symmetry breaking phases with long-range order is analyzed. The second and third parts of the paper concern resonating valence-bond (RVB) spin liquids. In these phases the relationship between various authors approaches: Laughlin-Oshikawa, Sutherland, Rokhsar and Kivelson, Read and Chakraborty and the Lieb-Schultz-Mattis-Affleck proposal is studied. The deep physical relation between the degeneracy property and the absence of stiffness is explained and illustrated numerically. A new conjecture is formed concerning the absolute absence of sensitivity of the spin liquid ground-states to any twist of the boundary conditions (thermodynamic limit). In the third part of the paper the relations between the quantum numbers of the degenerate multiplets of the spin liquid phases are obtained exactly. Their relationship with a topological property of the wave functions of the low lying levels of this spin liquid phase is emphasized. In spite of the degeneracy of the ground-state, we explain why these phases cannot exhibit spontaneous symmetry breaking. Received 19 December 2001     

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     

Effective Hamiltonians for holes in antiferromagnets: a new approach to implement forbidden double occupancy

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results. Received: 23 December 1997 / Accepted: 17 March 1998     

An investigation of the quantum J 1 - J 2 - J 3 model on the honeycomb lattice

We have investigated the quantum J ₁ - J ₂ - J ₃ model on the honeycomb lattice with exact diagonalizations and linear spin-wave calculations for selected values of J ₂ / J ₁ , J ₃ / J ₁ and antiferromagnetic (J ₁ > 0) or ferromagnetic (J ₁ < 0) nearest neighbor interactions. We found a variety of quantum effects: “order by disorder" selection of a Néel ordered ground-state, good candidates for non-classical ground-states with dimer long range order or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be Néel ordered. Comparing these results with those observed on the square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models. Received 17 November 2000 and Received in final form 21 January 2001     

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions

Phase separation in the strongly correlated Falicov-Kimball model in infinite dimensions is examined. We show that the phase separation can occur for any values of the interaction constant J^* when the site energy of the localized electrons is equal to zero. Electron-poor regions always have homogeneous state and electron-rich regions have chessboard state for , chessboard state or homogeneous state in dependence upon temperature for 0<J ^* <0.03 and homogeneous state for J ^* =0. For J ^* =0 and T=0, phase separation (segregation) occurs at .The obtained results are exact for the Bethe lattice with infinite number of the nearest neighbours. Received 1 December 1998 and Received in final form 12 April 1999     

Dynamical mean-field theory of a simplified double-exchange model

Simplified double-exchange model including transfer of the itinerant electrons with spin parallel to the localized spin in the same site and the indirect interaction J of kinetic type between localized spins is comprihensively investigated. The model is exactly solved in infinite dimensions. The exact equations describing the main ordered phases (ferromagnetic and antiferromagnetic) are obtained for the Bethe lattice with (z is the coordination number) in analytical form. The exact expression for the generalized paramagnetic susceptibility of the localized-spin subsystem is also obtained in analytical form. It is shown that temperature dependence of the uniform and the staggered susceptibilities has deviation from Curie-Weiss law. Dependence of Curie and Néel temperatures on itinerant-electron concentration is discussed to study instability conditions of the paramagnetic phase. Anomalous temperature behaviour of the chemical potential, the thermopower and the specific heat is investigated near the Curie point. It is found for J=0 that the system is unstable towards temperature phase separation between ferromagnetic and paramagnetic states. A phase separation connected with antiferromagnetic and the paramagnetic phases can occur only at . Zero-temperature phase diagram including the phase separation between ferromagnetic and antiferromagnetic states is given. Received 28 May 1999 and Received in final form 14 July 1999     

Thermal evolution of hole dynamics in the large-dimensional model

The dynamics of a single hole in the t - J model is solved exactly for all temperature, T, in the limit of large spatial dimensions, , using the Feenberg renormalized perturbation series. We focus in particular on single-particle spectra, together with optical and static hole conductivities. Explicit results are illustrated for a Bethe lattice, and exemplify the continuous thermal evolution of the underlying string picture from the T =0 string-pinned limit through to the paramagnetic phase. Quenched site-disorder is also readily incorporated, exact results thereby being obtained for the interplay between disorder and thermally-induced hole dynamics. Received 16 September 1998     

Antiferromagnetism of almost localized fermions: Evolution from Slater-type to Mott-Hubbard gap

We supplement (and critically overview) the existing extensive analysis of antiferromagnetic solution for the Hubbard model with a detailed discussion of two specific features, namely (i) the evolution of the magnetic (Slater) gap (here renormalized by the electronic correlations) into the Mott-Hubbard or atomic gap, and (ii) a rather weak renormalization of the effective mass by the correlations in the half-filled-band case, which contrasts with that for the paramagnetic case. The mass remains strongly enhanced in the non-half-filled-band case. We also stress the difference between magnetic and non-magnetic contributions to the gap. These results are discussed within the slave boson approach in the saddle-point approximation, in which there appears a non-linear staggered molecular field due to the electronic correlations that leads to the appearance of the magnetic gap. They reproduce correctly the ground-state energy in the limit of strong correlations. A brief comparison with the solution in the limit of infinite dimensions and the corresponding situation in the doubly-degenerate-band case with one electron per atom is also made. Received 16 December 2002 / Received in final form 5 February 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: ufspalek@if.uj.edu.pl     

Localization, Dirac fermions and Onsager universality

Disordered systems exhibiting exponential localization are mapped to anisotropic spin chains with localization length being related to the anisotropy of the spin model. This relates localization phenomenon in fermions to the rotational symmetry breaking in the critical spin chains. One of the intriguing consequence is that the statement of Onsager universality in spin chains implies universality of the localized fermions where the fluctuations in localized wave functions are universal. We further show that the fluctuations about localized nonrelativistic fermions describe relativistic fermions. This provides a new approach to understand the absence of localization in disordered Dirac fermions. We investigate how disorder affects well known universality of the spin chains by examining the multifractal exponents. Finally, we examine the effects of correlations on the localization characteristics of relativistic fermions. Received 28 September 2001 / Received in final form 30 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: isatija@nickel.nist.gov     

Electron-doping versus hole-doping in the 2D t-t' Hubbard model

We compare the one-loop renormalization group flow to strong coupling of the electronic interactions in the two-dimensional t-t'-Hubbard model with t' = - 0.3t for band fillings smaller and larger than half-filling. Using a numerical N-patch scheme ( N = 32, ..., 96) we show that in the electron-doped case with decreasing electron density there is a rapid transition from a d _{x2 - y2}-wave superconducting regime with small characteristic energy scale to an approximate nesting regime with strong antiferromagnetic tendencies and higher energy scales. This contrasts with the hole-doped side discussed recently which exhibits a broad parameter region where the renormalization group flow suggests a truncation of the Fermi surface at the saddle points. We compare the quasiparticle scattering rates obtained from the renormalization group calculation which further emphasize the differences between the two cases. Received 19 December 2000 and Received in final form 28 February 2001     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Dynamical spin and charge response functions in the doped two-dimensional Hubbard model

Dynamical properties of the spin and charge response functions in the doped two-dimensional Hubbard model are calculated by taking into account the drastic separation of the single-particle spectral function into the low-energy coherent and high-energy incoherent parts due to the strong Coulomb interaction. We show that this evolution of the electronic states is the origin of the broad and structureless feature in the charge response function. In the weak coupling regime the low-energy enhancement of the spin excitation is produced which can be explained within the random phase approximation. However, for the larger interaction close to the antiferromagnetic Stoner condition, the low-energy intensity of the spin excitation is suppressed. Received: 25 September 1997 / Revised: 19 December 1997 / Accepted: 9 January 1998     

Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z=3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments at large U/t. While NN sites show antiferromagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U=0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates. Received 8 February 1999 and Received in final form 14 June 1999     

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece [2,3] which show that two of these parameters, G and G _c, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for T _c and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at. Received 20 September 2000 and Received in final form 10 January 2001     

Fermionic representation of a symmetrically frustrated SU(3) model: Application to the Haldane-gap antiferromagnets

The one-dimensional spin 1 bilinear-biquadratic model is re-expressed in a symmetrically frustrated SU(3) model, which facilitates us to introduce a fermionic representation and related bond-operator mean-field theory. By analyzing the gap and the static spin susceptibility, we shows that this treatment can easily capture the commensurate and incommensurate Haldane gap phases.     

Remnant Fermi surface in a pseudogap regime of the two-dimensional Hubbard model at finite temperature

A precursor effect on the Fermi surface in the two-dimensional Hubbard model at finite temperatures near the antiferromagnetic instability is studied using three different itinerant approaches: the second order perturbation theory, the paramagnon theory (PT), and the two-particle self-consistent (TPSC) approach. In general, at finite temperature, the Fermi surface of the interacting electron systems is not sharply defined due to the broadening effects of the self-energy. In order to take account of those effects we consider the single-particle spectral function A(, 0) at the Fermi level, to describe the counterpart of the Fermi surface at T = 0. We find that the Fermi surface is destroyed close to the pseudogap regime due to the spin-fluctuation effects in both PT and TPSC approaches. Moreover, the top of the effective valence band is located around = (π/2,π/2) in agreement with earlier investigations on the single-hole motion in the antiferromagnetic background. A crossover behavior from the Fermi-liquid regime to the pseudogap regime is observed in the electron concentration dependence of the spectral function and the self-energy. Received 8 September 2000 and Received in final form 20 December 2000     

Aging effects and dynamic scaling in the 3D Edwards-Anderson spin glasses: a comparison with experiments

We present a detailed study of the scaling behavior of correlations functions and AC susceptibility relaxations in the aging regime in three-dimensional spin glasses. The agreement between simulations and experiments is excellent confirming the validity of the full aging scenario with weak sub-aging effects. Received 21 December 2000 and Received in final form 22 February 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