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We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.

The main properties of realistic models for manganites are studied using analytic mean-field approximations and computational numerical methods, focusing on the two-orbital model with electrons interacting through Jahn-Teller (JT) phonons and/or Coulombic repulsions. Analyzing the model including both interactions by the combination of the mean-field approximation and the exact diagonalization method, it is argued that the spin-charge-orbital structure in the insulating phase of the purely JT-phononic model is not qualitatively changed by the inclusion of the Coulomb interactions. As an important application of the present mean-field approximation, the CE-type AFM state, the charge-stacked structure along the z-axis, and the (3x^2-r^2)/(3y^2-r^2)-type orbital ordering are successfully reproduced based on the JT-phononic model for the half-doped manganite. Topological arguments and the relevance of the Heisenberg exchange among localized t_{\rm 2g} spins explains why the nearest-neighbor Coulomb interaction does not destroy the charge stacking structure. It is also verified that the phase-separation tendency is observed both in purely JT-phononic and purely Coulombic models in the vicinity of the hole undoped region, as long as realistic hopping matrices are used. This highlights the qualitative similarities of both approaches, and the relevance of mixed-phase tendencies in the context of manganites. In addition, the rich and complex phase diagram of the two-orbital Coulombic model in one dimension is presented. Our results provide robust evidence that Coulombic and JT-phononic approaches to manganites are not qualitatively different ways to carry out theoretical calculations, but they share a variety of common features., 23 pages, Revtex, with 15 figures embedded in the text. Submitted to Phys. Rev. B

Spin models that have been proposed to describe dimerized chains, ladders, two dimensional antiferromagnets, and other compounds are here studied when some spins are replaced by spinless vacancies, such as it occurs by $Zn$ doping. A small percentage of vacancies rapidly destroys the spin gap, and their presence induces enhanced antiferromagnetic correlations near those vacancies. The study is performed with computational techniques which includes Lanczos, world-line Monte Carlo, and the Density Matrix Renormalization Group methods. Since the phenomenon of enhanced antiferromagnetism is found to occur in several models and cluster geometries, a common simple explanation for its presence may exist. It is argued that the resonating-valence-bond character of the spin correlations at short distances of a large variety of models is responsible for the presence of robust staggered spin correlations near vacancies and lattice edges. The phenomenon takes place regardless of the long distance properties of the ground state, and it is caused by a ``pruning'' of the available spin singlets in the vicinity of the vacancies. The effect produces a broadening of the low temperature NMR signal for the compounds analyzed here. This broadening should be experimentally observable in the structurally dimerized chain systems $Cu(NO_3)_2\cdot2.5H_2O$, $CuWO_4$, $(VO)_2P_2O_7$, and $Sr_{14}Cu_{24}O_{41}$, in ladder materials such as $Sr Cu_2 O_3$, in the spin-Peierls systems $CuGeO_3$ and $NaV_2 O_5$, and in several others since it is a universal effect common to a wide variety of models and compounds., 18 pages revtex with 26 figures included

The Kondo lattice Hamiltonian with ferromagnetic Hund's coupling as a model for manganites is investigated. The classical limit for the spin of the (localized) $t_{2g}$ electrons is analyzed on lattices of dimension 1,2,3 and $\infty$ using several numerical methods. The phase diagram at low temperature is presented. A regime is identified where phase separation occurs between hole undoped antiferromagnetic and hole-rich ferromagnetic regions. Experimental consequences of this novel regime are discussed. Regions of incommensurate spin correlations have also been found. Estimations of the critical temperature in 3D are compatible with experiments., Accepted in Phys. Rev. Letters

The phase diagram of two coupled anisotropic spin-1/2 Heisenberg chains forming a ladder is studied via the finite-size machinery arising from conformal invariance. Our results show that this system has similar behaviour to the anisotropic spin-1 Heisenberg chain. Both models for low values of anisotropies have a massless phase of Gaussian type, governed by a c = 1 conformal field theory. The operator that destroys the massless phase in these models is the same as in the Gaussian picture. We also verify that the massive phase in the anisotropic Heisenberg ladder has the same type of nonlocal order as that in the spin-1 Heisenberg chain.

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S') SU(2) operator interacting with a XXZ like interaction (anisotropy $\Delta$). Our results indicate universal properties for all these chains. The whole phase, $1>\Delta>-1$, where the models change from ferromagnetic $( \Delta=1 )$ to ferrimagnetic $(\Delta=-1)$ behaviour is critical. Along this phase the critical fluctuations are ruled by a c=1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions., Comment: 21 pages, standard LaTex, to appear in J.Phys.A:Math.Gen

The phase diagram of the XXZ chain is calculated under the influence of homogeneous and staggered magnetic fields. The model has a rich phase structure with three types of phases. A fully ferromagnetic phase, an antiferromagnetic phase and a massless phase with partial ferromagnetic and antiferromagnetic order. This massless phase's critical fluctuations are governed by a conformal field theory with central charge c=1. When the sigma z-anisotropy Delta is zero the model is exactly integrable through a Jordan-Wigner fermionization and our results are analytic. For Delta not=0 our analysis is done numerically using lattice sizes up to M=20. Our results show that for -1

Made available in DSpace on 2022-04-29T00:49:43Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-08-15 We have used the density-matrix renormalization group method to study the ground-state properties of the symmetric periodic Anderson model in one dimension. We have considered lattices with up to Ns=50 sites, and electron densities ranging from quarter to half filling. Through the calculation of energies, correlation functions, and their structure factors, together with careful extrapolations (toward Ns→ ), we were able to map out a phase diagram Uvsn, where U is the electronic repulsion on f orbitals, and n is the electronic density, for a fixed value of the hybridization. At quarter filling, n=1, our data is consistent with a transition at U c1 2, between a paramagnetic (PM) metal and a spin-density-wave (SDW) insulator; overall, the region U 2 corresponds to a PM metal for all n

A study is made of the anisotropic biquadratic spin-1 Hamiltonian introduced by Batchelor et al. (1990). This model can be represented as a sum of operators satisfying a Temperley-Lieb algebra. Its critical behaviour is explored by using the relations between mass-gap amplitudes and critical exponents predicted by conformal invariance. The model, like in the XXZ chain, is found to exhibit a line of continuously varying exponents. By comparing its eigenspectrum with that of the XXZ Hamiltonian, several exact values are predicted.

We discuss the interplay between electronic correlations and an underlying superlattice structure in determining the period of charge density waves (CDW's), by considering a one-dimensional Hubbard model with a repeated (non-random) pattern of repulsive (U>0) and free (U=0) sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wavevectors, k_F*, and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from q*=0 to ��, but also due to sharp 2k_F*-4k_F* transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems., 4 pages, 5 figures, to appear in Phys Rev B

This is an introductory course to the Lanczos Method and Density Matrix Renormalization Group Algorithms(DMRG), two among the leading numerical techniques applied in studies of low-dimensional quantum models. The idea of studying the models on clusters of a finite size in order to extract their physical properties is briefly discussed. The important role played by the model symmetries is also examined. Special emphasis is given to the DMRG., Comment: 36 pages, 4 figures, standard LaTex, Brazilian School on Statistical Mechanics (2002), PDF and PS files available at http://www.sbf.if.usp.br/bjp

We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-U couplings arranged in a repeated pattern of repulsive (i.e., U>0) and free (U=0) sites. Density Matrix Renormalization Group (DMRG) diagonalization of finite systems is used to calculate the local moment and the magnetic structure factor in the ground state. We have found four regimes for magnetic behavior: uniform local moments forming a spin-density wave (SDW), `floppy' local moments with short-ranged correlations, local moments on repulsive sites forming long-period SDW's superimposed with short-ranged correlations, and local moments on repulsive sites solely with long-period SDW's; the boundaries between these regimes depend on the range of electronic densities, rho, and on the SL aspect ratio. Above a critical electronic density, rho_{uparrow downarrow}, the SDW period oscillates both with rho and with the spacer thickness. The former oscillation allows one to reproduce all SDW wave vectors within a small range of electronic densities, unlike the homogeneous system. The latter oscillation is related to the exchange oscillation observed in magnetic multilayers. A crossover between regimes of `thin' to `thick' layers has also been observed., 9 two-column pages, 10 figures

Spin incommensurability (IC) has been recently experimentally discovered in the hole-doped Ni-oxide chain compound ${\mathrm{Y}}_{2\ensuremath{-}x}{\mathrm{Ca}}_{x}{\mathrm{BaNiO}}_{5}$ [G. Xu et al., Science 289, 419 (2000)]. Here a two orbital model for this material is studied using computational techniques. Spin IC is observed in a wide range of densities and couplings. The phenomenon originates in antiferromagnetic correlations ``across holes'' dynamically generated to improve hole movement, as it occurs in the one-dimensional Hubbard model and in recent studies of the two-dimensional extended $t\ensuremath{-}J$ model. The close proximity of ferromagnetic and phase-separated states in parameter space is also discussed.

We applied the Density Matrix Renormalization Group to the XXZ spin-1 quantum chain. In studing this model we aim to clarify controversials about the point where the massive Haldane phase appears., Comment: 2 pages (standart LaTex), 1 figure (PostScript) uuencoded

We discuss the comments presented by Okamoto and Nomura about the phase diagram of the XXZ chain under the influence of an external staggered magnetic field, reported by Alcaraz and Malvezzi.

The phase diagram of the ferromagnetic Kondo model for manganites was recently investigated using computational techniques by Yunoki et al. [Phys. Rev. Lett. 80, 845 (1998)]. In dimensions 1, 2, and $\ensuremath{\infty}$ and using classical localized spins, this study suggested a rich low-temperature phase diagram with three dominant regions: (i) a ferromagnetic phase, (ii) phase separation between hole-undoped antiferromagnetic and hole-rich ferromagnetic domains, and (iii) a phase with incommensurate spin correlations. The purpose of the present paper is twofold: (a) First, a variety of computational results is here provided to substantiate and supplement the previous results by Yunoki et al., investigating a complementary region of couplings and densities; (b) second, studies using the Lanczos algorithm and the density matrix renormalization group method applied to chains with localized spin 1/2 (with and without Coulombic repulsion for the mobile electrons) and spin 3/2 degrees of freedom are discussed. The overall conclusion is that using fully quantum mechanical localized spins in one-dimensional systems, the phase diagram of the model is similar to the result obtained using classical ${t}_{2g}$ spins. This result provides support of the use of classical localized spins in more complicated problems, such as in dimensions larger than 1 and/or including phononic and orbital degrees of freedom, where the use of classical spins is crucial to simplify the complexity of the problem.

We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point., Foundation for Development of UNESP (FUNDUNESP); Sao Paulo Research Foundation (FAPESP); National Counsel of Technological and Scientific Development (CNPq); National Institute for Science and Technology of Quantum Information (INCT-IQ); Minas Gerais Research Foundation (FAPEMIG); CNPq; INCT-IQ