First and second order ferromagnetic transition at in a 1D itinerant system

We consider a modified version of the one-dimensional Hubbard model, the t ₁ - t ₂ Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t₂ to t₁. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T =0, the second order transition is a quantum magnetic critical point. Received 21 July 1999     

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     

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     

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     

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte-Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increase of the static S-wave pair correlation with decreasing temperature, which depends weakly on the band filling in the explored temperature range, is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. Using both our data and previously published results, we show that the evidence for this transition is weak: If it exists, its temperature is very low. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Padé approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data. Received: 30 October 1996 / Revised: 23 October 1997 / Accepted: 29 January 1998     

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     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

Spectral densities of response functions for the O(3) symmetric Anderson and two channel Kondo models

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln divergence found in the low frequency behaviour of the T=0 dynamic susceptibility. Received 29 January 1999     

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     

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.     

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     

Charge density waves and bond order waves in a quarter filled extended Hubbard ladder

We investigate the phase diagram of a quarter filled Hubbard ladder with nearest-neighbor Coulomb repulsion using bosonization and renormalization group approach. Focusing on the strong-repulsion regime, we discuss the effect of an interchain exchange interaction J and interchain repulsion V on the possible ground states of the system and charge order configurations. Since the spin excitations always possess a gap, we find competing bond-order wave and charge density wave phases as possible ground states of the ladder model. We discuss the elementary excitations in these various phases and point an analogy between the excitations on some of these phases and those of a Kondo-Heisenberg insulator. We also study the order of the quantum phase transitions between the different ground states of the system. We obtain second order transitions in the Ising or SU(2)₂ universality class or first order transitions. We map the complete phase diagram in the J –V plane by integrating perturbative renormalization-group equations. Finally, we discuss the effect of doping away from half-filling and the effect of an applied magnetic field.     

Quantum XY spin glass model with planar Dzyaloshinskii-Moriya interactions in longitudinal field

In the replica symmetric approximation and static limit in Matsubara “imaginary time”, the quantum XY spin glass model with planar Dzyaloshinskii-Moriya interaction in longitudinal field is investigated. Several thermodynamic quantities are calculated numerically as well as spin self-interaction and spin glass order parameter for spin S=1/2. It is shown that the entropy is not independent of the field. A crossover behavior of the specific heat depending on temperature is found. There is a deviation from the parabolic approximation, C/T=A+Bh ² . Received 11 March 1998     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Phase diagram of an asymmetric spin ladder

We investigate an asymmetric zigzag spin ladder with different exchange integrals on both legs using bosonization and renormalization group approaches. When the leg exchange integrals and frustration both are sufficiently small, renormalization group analysis shows that the Heisenberg critical point flows to an intermediate-coupling fixed point with gapless excitations and a vanishing spin velocity. When they are large, a spin gap opens and a dimer liquid is realized. Here, we find a continuous manifold of Hamiltonians with dimer product ground states, interpolating between the Majumdar-Ghosh and sawtooth spin-chain model.     

Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behavior

A brief account of the zero temperature magnetic response of a system of strongly correlated electrons in strong magnetic field is given in terms of its quasiparticle properties. The scenario is based on the paramagnetic phase of the half-filled Hubbard model, and the calculations are carried out with the dynamical mean field theory (DMFT) together with the numerical renormalization group (NRG). As well known, in a certain parameter regime one finds a magnetic susceptibility which increases with the field strength. Here, we analyze this metamagnetic response based on Fermi liquid parameters, which can be calculated within the DMFT-NRG procedure. The results indicate that the metamagnetic response can be driven by field-induced effective mass enhancement. However, also the contribution due to quasiparticle interactions can play a significant role. We put our results in context with experimental studies of itinerant metamagnetic materials.