Exact Diagonalization Results Research Articles

Elementary excitations in one-dimensional spin-orbit models: Neutral and charged solitons and their bound states

We study, both numerically and variationally, the interplay between different types of elementary excitations in the model of a spin chain with anisotropic spin-orbit coupling, in the vicinity of the "dimer line" with an exactly known dimerized ground state. Our variational treatment is found to be in a qualitative agreement with the exact diagonalization results. Soliton pairs are shown to be the lowest excitations only in a very narrow region of the phase diagram near the dimer line, and the phase transitions are always governed by magnon-type excitations which can be viewed as soliton-antisoliton bound states. It is shown that when the anisotropy exceeds certain critical value, a new phase boundary appears. In the doped model on the dimer line, the exact elementary charge excitation is shown to be a hole bound to a soliton. Bound states of those "charged solitons" are studied; exact solutions for N-hole bound states are presented.

Variational study of the ground state energy of the E−b 1 , b 2 Jahn-Teller system

In this paper a variational method for the ground state energy approximation of theE−b 1,b 2 Jahn-Teller system is presented. This method is based on the choice of a suitable variational ground state wave function. This trial wave function — a correlated squeezed state — is used to account for the correlation and anharmonicity of the interaction between the two vibrational modes; the anharmonicity of both modes is taken into account by the squeeze effects of these modes. The ground state of mode 1 in this trial wave function is considered as a linear combination of the two displaced harmonic oscillators. The ground state energies for the linearE - e Jahn-Teller system calculated by this method are not only in good agreement with the exact diagonalization results, but they are also better than those from the previous analytical studies. Another conclusion which results from the presented model is the following one: the squeezing effect of mode 1 for the linearE - e Jahn-Teller system is substantially smaller, in contrast with the results which are presented in the previous analytical studies.

COMMENSURATE VERSUS INCOMMENSURATE SPIN-ORDERING IN THE TRIANGULAR HUBBARD MODEL

The presence of incommensurate spin structures in the half-filled triangular Hubbard model, where frustration leads to a competition among different magnetic phases, is investigated using both the slave-boson technique, and exact diagonalization of finite clusters. We also investigate the metal-insulator transition which, due to the lack of perfect nesting, takes place at a finite value of U. Within the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing further the interaction, a linear spin-density-wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition towards an antiferromagnetic insulator. No trace of the intermediate phases is instead found in the exact diagonalization results.

Influence of intersite CuO repulsion on hole binding and pairing correlations in the three-band Hubbard model

The hole binding energy and pairing correlations are calculated in the three-band Hubbard model by using the constrained-path Monte Carlo (CPMC) method. In the physically relevant region, we investigated effects of CuO Coulomb repulsion V pd on these two properties. Simulations were performed on lattices of 2×2, 4×2 and 6×4 unit cells. For the 2×2 unit cell, the CPMC results are in good agreement with exact diagonalization results. For it we found that the hole binding energy clearly increases with the nearest-neighbor Coulomb repulsion V pd , but for larger systems it increases only slightly. For the extended s-wave channel, we found that the pairing correlations and vertex contributions increase slightly with an increase of V pd , while for the d x 2− y 2 -wave channel both tend to decrease.

CANONICAL TRANSFORMATION OF THE HUBBARD MODEL AND W = 0 PAIRING: COMPARISON WITH EXACT DIAGONALIZATION RESULTS

We have recently developed a canonical transformation of the Hubbard and related models, valid for systems of arbitrary size and for the full plane; this is particularly suited to study hole pairing. In this work we show that exact diagonalization results of the one band Hubbard model for small clusters with periodic boundary conditions agree well with the analytical ones obtained by means of our canonical transformation. In the presence of a pairing instability, the analytic approach allows us to identify the Cooper pairs. They are W = 0 pairs, that is, singlet two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. Indeed, we find that the Coulomb interaction effects on W = 0 pairs are dynamically small, and repulsive or attractive, depending on the filling.

Current-spin-density-functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress the persistent current in a characteristic way.

RVB description of the low-energy singlets of the spin 1/2 kagomé antiferromagnet

{Extensive calculations in the short-range RVB (Resonating valence bond) subspace on both the trimerized and the regular (non-trimerized) Heisenberg model on the kagome lattice show that short-range dimer singlets capture the specific low-energy features of both models. In the trimerized case the singlet spectrum splits into bands in which the average number of dimers lying on one type of bonds is fixed. These results are in good agreement with the mean field solution of an effective model recently introduced. For the regular model one gets a continuous, gapless spectrum, in qualitative agreement with exact diagonalization results.

C-axis optical conductivity in cuprates

We investigate the c-axis optical conductivity and DC resistivity of cuprate superconductors in the normal state. Assuming that the interlayer hopping is incoherent we express the conductivity with planar spectral functions obtained (i) from angle-resolved photoemission experiments (ARPES), (ii) using marginal Fermi liquid (MFL) ansatz, and (iii) with the finite-temperature Lanczos method for finite two-dimensional systems described by the t– J model. In the optimally doped regime anomalous relaxation rate τ c −1∝ ω+ ξ c T found by Prelovšek et al. (Phys. Rev. Lett. 81 (1998) 3745) is analytically reproduced with the use of the marginal Fermi liquid ansatz for the self energy with parameters obtained from the exact diagonalization results. A semimetallic-like behavior of ρ c( T) in the low doping regime emerges due to a pseudo-gap opening in the density of states.

Interacting electrons in a 2D quantum dot

The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons. The results are compared with those of the perturbation theory. Our numerical results agree reasonably well for small values of the dimensionless coupling constant λ= a/ a B where a is the dot radius and a B is the effective Bohr radius. Exact diagonalization results are compared with the classical predictions, and they are found to be almost coincident for large λ values.

Quantum spin chains in a magnetic field

We demonstrate that the ``worm'' algorithm allows very effective and precise quantum Monte Carlo (QMC) simulations of spin systems in a magnetic field, and its auto-correlation time is rather insensitive to the value of H at low temperature. Magnetization curves for the $s=1/2$ and $s=1$ chains are presented and compared with existing Bethe ansatz and exact diagonalization results. From the Green function analysis we deduce the magnon spectra in the s=1 system, and directly establish the "relativistic" form E(p)=(\Delta ^2 +v^2 p^2)^{1/2} of the dispersion law.

Optimal coupled-cluster approximation for the ground-state properties of a spin-boson model

In the present work we have developed an optimal coupled-cluster approximation, which can take care of both the accuracies of the ground-state energy and the wavefunction estimates, for the ground state of a two-state system coupled to a dispersionless boson bath. This new approach is also able to give a tight upper bound to the ground-state energy of the system. Up to the fourth level of this approximation our results show excellent agreement with the numerical exact diagonalization results. In particular, our results suggest no discontinuous localization-delocalization transition of the two-state system. This is consistent with the exact result.

Exact-diagonalization study on the effect of the long-range Coulomb interaction to the superconducting ground state in the two-chain Hubbard model

We present exact-diagonalization results clearly indicating that the long-range part of Coulomb interaction does not sweep away the superconducting region of the two-chain Hubbard model driven by the short-range part. When the model contains the nearest-neighbor Coulomb interaction both for the interchain and the intrachain directions, the region of developed superconducting correlations in the ground state is reduced. The CDW correlation is found to increase, intervening with the competition between superconductivity and CDW. When we include the long-range Coulomb interaction of the type of 1/ r, the instability to the CDW state weakens with the superconducting region recovered to some extent compared with the above case.

Thermodynamics of quantum Heisenberg spin chains

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.

Monte Carlo comparison of quasielectron wave functions

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions $\ensuremath{\nu}=1/3,$ 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite-fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interactions the results obtained using these two wave functions are essentially the same, though the energy gap obtained using the composite-fermion quasielectron is slightly smaller, and closer to extrapolated exact-diagonalization results.

Hole pairing and flux quantization in modelCu-O clusters

In the three-band Hubbard model, the fully symmetric Cu-O clusters with a central Cu and appropriate hole numbers have many-body ground states in which holes are paired. Here we investigate the mechanism of pairing, focusing on clusters with ≤ 21 atoms and 4 holes. We show that spin-flip diagrams yield the effective interaction. The analysis agrees with the results of exact diagonalization and shows that singlet-triplet splitting measures the strength of the pairing interaction. Moreover, the quantization at half-integer values of a magnetic text flux is consistent with supercon-ducting pairing.

Application of the SD Technique for Solving a BCS-Reduced Hubbard like Hamiltonian

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the d x2-y2 channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We present a review of the technical details of the application of the stochastic diagonalization algorithm on this problem. To verify our results obtained with the stochastic diagonalization, they are compared with the exact diagonalization results. In order to show the convergence of the stochastic diagonalization we give a detailed analysis of the behavior of physical properties with increasing number of states. Finally we study superconductivity in this BCS-reduced Hubbard model. As an indicator of superconductivity we use the occurrence of Off Diagonal Long Range Order. We study the scaling behavior of this model for various attractive interactions and in addition the dependence of the superconducting correlation functions from the filling of the system.

Low density electron pairs in the extended Hubbard model

We study the extended Hubbard model in the parameter region where it exhibits superconducting instabilities. The model is defined by onsite and nearest-neighbor Coulomb interactions U and V, and hopping integral t. We calculate pair binding energies for various finite clusters by performing exact diagonalization of the Hamiltonian. We show results for one-dimensional chains and discuss results for 4 × 4, 6 × 6, and 8 × 8 two-dimensional square lattices. Results of solving the BCS equation for the pair binding energy as functions of carrier density n, and Coulomb interactions U and V, are compared with the exact diagonalization results. In the dilute concentration limit ( n → 0), the BCS equation is expected to be exact and, in the low electron density region, the results for the pair binding energy are found to be in fairly good agreement with the exact solutions.

Charge and spin excitations of insulating lamellar copper oxides

A consistent description of low-energy charge and spin responses of the insulating ${\mathrm{Sr}}_{2}$${\mathrm{CuO}}_{2}$${\mathrm{Cl}}_{2}$ lamellar system is found in the framework of a one-band Hubbard model which besides U includes hoppings up to third nearest neighbors. By combining mean-field calculations, exact diagonalization results, and quantum Monte Carlo simulations, we analyze both charge and spin degrees of freedom responses as observed by optical conductivity, angular-resolved photoemission spectroscopy Raman and inelastic neutron-scattering experiments. Within this effective model, long-range hopping processes flatten the quasiparticle band around (0,\ensuremath{\pi}). We calculate also the nonresonant ${\mathrm{A}}_{1\mathrm{g}}$ and ${\mathrm{B}}_{1\mathrm{g}}$ Raman profiles and show that the latter is composed by two main features, which are attributed to two- and four-magnon scattering.

Quantitative study of large composite-fermion systems

Quantitative investigations of the fractional quantum Hall effect (FQHE) have been limited in the past to systems containing typically fewer than 10{endash}12 particles, except for the 1/(2p+1) Laughlin states. We develop a method, using the framework of the composite-fermion theory, that enables a treatment of much bigger systems and makes it possible to obtain accurate quantitative information for other incompressible states as well. After establishing the validity of this method by comparison with few-particle exact-diagonalization results, we compute the ground-state energies and transport gaps for a number of FQHE states. {copyright} {ital 1997} {ital The American Physical Society}

Optimal coupled-cluster approximation for the linear E- e Jahn-Teller effect

By introducing a slight modification to the successive coupled-cluster approximation, we have developed an optimal coupled-cluster approximation, which can take care of both the accuracies of the ground-state energy and wavefunction estimates, for the ground state of the linear E- e Jahn-Teller effect. Over the whole range of the coupling parameter, our results up to the third level of approximation show good agreement with the exact numerical diagonalization results and are better than those from earlier analytical treatments. The mathematical treatment in this work is simple and could be easily extended to the studies of other fermion-boson interacting systems.