Lanczos Exact Diagonalization Research Articles

Spectral function of the one-dimensional Holstein model at half filling

The one-electron spectral function of the one-dimensional spin-$1∕2$ Holstein model at half filling is computed by use of the cluster perturbation theory. The cluster Green's function is obtained by the Lanczos exact diagonalization method within an optimized phonon approach. It is shown that the method allows reliable calculations using a relatively small size cluster and a few optimal phonon bases for the system from weak to strong electron-phonon coupling. In the strong-coupling limit, the spectral function shows the excitation behavior of a bipolaron state with a large gap at the Fermi surface. However, the obtained spectral function displays a metallic character in the weak-coupling regime, which is in accord with the suggestion that the Peierls gap is suppressed by quantum fluctuation of the phonons.

Influence of the spin quantum numbers on the zero-temperature phase transition in the square-latticeJ–J' model

We investigate the phase diagram of the Heisenberg antiferromagneton the square lattice with two different nearest-neighbour bondsJ and J' (J–J' model) at zero temperature. The model exhibits a quantum phase transition at a criticalvalue between a semi-classically ordered Néel and a magnetically disordered quantumparamagnetic phase of valence-bond type, which is driven by local singlet formation onJ' bonds. We study the influence of spin quantum numbers on this phase transition by means of a variational mean-field approach, the coupled clustermethod and the Lanczos exact-diagonalization technique. We present evidence that thecritical value increases with growing s according to .

FINITE-SIZE SPIN-WAVE THEORY OF A COLLINEAR ANTIFERROMAGNET

The ground-state and low-energy properties of the two-dimensional J1-J2 Heisenberg model in the collinear phase are investigated using finite-size spin-wave theory [Q. F. Zhong and S. Sorella, Europhys. Lett.21, 629 (1993)], and Lanczos exact diagonalizations. For spin one-half — where the effects of quantization are the strongest — the spin-wave expansion turns out to be quantitatively accurate for J2/J1≳0.8. In this regime, both the magnetic structure factor and the spin susceptibility are very close to the spin-wave predictions. The spin-wave estimate of the order parameter in the collinear phase, m†≃0.3, is in remarkable agreement with recent neutron scattering measurements on Li 2 VOSiO 4.

Stripes and holes in a two-dimensional model of spinless fermions or hardcore bosons

We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls between ordered domains) are a favorable way to dope this system below half-filling. The problem of a single stripe can be mapped to a spin-1/2 chain, which allows understanding of its elementary excitations and calculation of the stripe's effective mass for transverse vibrations. Using Lanczos exact diagonalization, we investigate the excitation gap and dispersion of a hole on a stripe, and the interaction of two holes. We also study the interaction of two, three, and four stripes, finding that they repel, and the interaction energy decays with stripe separation as if they are hardcore particles moving in one (transverse) direction. To determine the stability of an array of stripes against phase separation into particle-rich phase and hole-rich liquid, we evaluate the liquid's equation of state, finding the stripe-array is not stable for bosons but is possibly stable for fermions.

Ground state of a Heisenberg chain with next-nearest-neighbor bond alternation

We investigate the ground-state properties of the spin-half ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg chain with a next-nearest-neighbor spin-Peierls dimerization using conformal field theory and Lanczos exact diagonalizations. In agreement with the results of a recent bosonization analysis by Sarkar and Sen [Phys. Rev. B $65,$ 172408 (2002)], we find that for small frustration ${(J}_{2}{/J}_{1})$ the system is in a Luttinger spin-fluid phase, with gapless excitations, and a finite spin-wave velocity. In the regime of strong frustration the ground state is spontaneously dimerized and the bond alternation reduces the triplet gap, leading to a slight enhancement of the critical point separating the Luttinger phase from the gapped one. An accurate determination of the phase boundary is obtained numerically from the study of the excitation spectrum.

Magnetic phases of the mixed-spinJ1−J2Heisenberg model on a square lattice

We study the zero-temperature phase diagram and the low-energy excitations of a mixed-spin ($S_1>S_2$) $J_1-J_2$ Heisenberg model defined on a square lattice by using a spin-wave analysis, the coupled cluster method, and the Lanczos exact-diagonalization technique. As a function of the frustration parameter $J_2/J_1$ ($ >0$), the phase diagram exhibits a quantized ferrimagnetic phase, a canted spin phase, and a mixed-spin collinear phase. The presented results point towards a strong disordering effect of the frustration and quantum spin fluctuations in the vicinity of the classical spin-flop transition. In the extreme quantum system $(S_1,S_2)=(1,{1/2})$, we find indications of a new quantum spin state in the region $0.46< J_2/J_1<0.5$

Geometric (Berry) phases and statistical transmutation in the two-dimensional systems of antiferromagnetically correlated electrons

Focusing on the hole-doped two-dimensional systems of strongly correlated electrons, we examine the geometric phases which arise as a result of polaron transport around closed loops. It is of interest to see differences in the geometric phases between the two different systems of antiferromagnets, the Ising antiferromagnets and the Heisenberg antiferromagnets. For this study we apply the Lanczos exact diagonalization method to the Holstein–Hubbard, Holstein- tJ, and Holstein- tJ z models. It is shown from this study that the transverse spin interactions (fluctuations) are responsible for the generation of non-trivial geometric phases for the Heisenberg antiferromagnets, unlike the case of the Ising antiferromagnets.

Metallic state driven by frustrated electronic correlation in Cu-O double chain ofPrBa2Cu4O8

A proposal is made that the metallic state observed in the Cu-O double chain unit of ${\mathrm{PrBa}}_{2}{\mathrm{Cu}}_{4}{\mathrm{O}}_{8}$ is a peculiar state driven by geometrical frustration. We treat one-dimensional 1/4-filled extended Hubbard models with competing intersite Coulomb interactions appropriate for this compound, and estimate the charge gap using Lanczos exact diagonalization method. It is argued that the charge ordered insulating states, stabilized in the absence of frustration, can be ``melted'' when the degree of frustration is large so that a metallic state is realized. In the limit of large on-site Coulomb interaction U, the systems can be mapped onto one-dimensional $S=1/2\mathrm{XXZ}$ models, where our metallic state corresponds to a spin-liquid state due to the competing z component of the exchange couplings.

Peierls bond distortion in substituted polyacetylenes

Peierls lattice distortion has been investigated in substituted polyacetylenes. We find that the Peierls dimerization could be suppressed by the substitution of hydrogen atoms with phenyl or methyl. A study on an oligomer by a Lanczos exact diagonalization algorithm indicates that the inclusion of Hubbard repulsion does not change the result. The expected quadrimerization, which is required by the Peierls theorem, does not appear in poly(methyl-acetylene).

Lattice polaron formation: Effects of nonscreened electron-phonon interaction

We explore the quasiparticle properties of lattice polarons on the basis of a quite general electron-phonon Hamiltonian with a long-range displacement-type of interaction. To treat the dynamical quantum phonons without significant loss of accuracy we adapt an exact Lanczos diagonalization method and compute various static and dynamical quantities, such as the electron-lattice correlation function, the polaron band dispersion, the effective polaron mass, the kinetic energy, the single-particle spectral function, and the optical conductivity, on finite one-dimensional lattices for a wide range of model parameters. We compare the results with those obtained for the standard Holstein model with short-range electron-phonon interaction only.

Born effective charge reversal and metallic threshold state at a band insulator-Mott insulator transition

We study the quantum phase transition between a band (“ionic”) insulator and a Mott-Hubbard insulator, realized at a critical value in a bipartite Hubbard model with two inequivalent sites, whose on-site energies differ by an offset . The study is carried out both in D=1 and D=2 (square and honeycomb lattices), using exact Lanczos diagonalization, finite-size scaling, and Berry's phase calculations of the polarization. The Born effective charge jump from positive infinity to negative infinity previously discovered in D=1 by Resta and Sorella is confirmed to be directly connected with the transition from the band insulator to the Mott insulating state, in agreement with recent work of Ortiz et al. In addition, symmetry is analysed, and the transition is found to be associated with a reversal of inversion symmetry in the ground state, of magnetic origin. We also study the D=1 excitation spectrum by Lanczos diagonalization and finite-size scaling. Not only the spin gap closes at the transition, consistent with the magnetic nature of the Mott state, but also the charge gap closes, so that the intermediate state between the two insulators appears to be metallic. This finding, rationalized within Hartree-Fock as due to a sign change of the effective on-site energy offset for the minority spin electrons, underlines the profound difference between the two insulators. The band-to-Mott insulator transition is also studied and found in the same model in D=2. There too we find an associated, although weaker, polarization anomaly, with some differences between square and honeycomb lattices. The honeycomb lattice, which does not possess an inversion symmetry, is used to demonstrate the possibility of an inverted piezoelectric effect in this kind of ionic Mott insulator.

Effects of nonmagnetic impurities on optical conductivity in strongly correlated systems

Effects of nonmagnetic impurities on optical conductivity in the systems of antiferromagnetically correlated electrons are examined based on the Lanczos exact diagonalization scheme. As a result of resonant scattering a low-frequency peak in the optical conductivity is predicted to occur in the presence of the nonmagnetic impurities, which is consistent with the observed normal-state optical conductivity of ${\rm YBa_2}({\rm Cu}_{1-x}{\rm Zn}_x)_3{\rm O}_{7-\delta}$. In addition, a relatively high and broad peak is found to occur at a high frequency region as a consequence of the Heisenberg interaction between electrons, in agreement with observation in the peak position.

Lanczos exact diagonalization study of field-induced phase transitions for Ising and Heisenberg antiferromagnets

Using an exact diagonalization treatment of Ising and Heisenberg model Hamiltonians, we study field-induced phase transition for two-dimensional antiferromagnets. For the system of Ising antiferromagnet the predicted field-induced phase transition is of first order, while for the system of Heisenberg antiferromagnet it is the second-order transition. We find from the exact diagonalization calculations that the second-order phase transition (metamagnetism) occurs through a spin-flop process as an intermediate step.

Ground-state phase diagram of the one-dimensional dimerizedt−Jmodel at quarter filling

The ground state of the one-dimensional dimerized $t\ensuremath{-}J$ model at quarter filling is studied by a Lanczos exact-diagonalization technique on small clusters. We calculate the charge gap, spin gap, binding energy, Tomonaga-Luttinger-liquid parameter, Drude weight, anomalous flux quantization, etc. We thereby show that the two types of dimerization, i.e., a dimerization of hopping integral and a dimerization of exchange interaction play a mutually competing role in controlling the ground state of the system and this leads to the emergence of various phases including the Mott insulating, Tomonaga-Luttinger-liquid, and spin-gap-liquid phases. The ground-state phase diagram of the model is given on the parameter space of the dimerizations.

EXCITON STATES AND LUMINESCENT PROPERTIES IN ONE-DIMENSIONAL SEMICONDUCTOR POLYMER AND THE EFFECT OF LATTICE DISTORTION

We use Lanczos exact diagonalization method to analyze the energy and the wave functions of exciton states in one-dimensional semiconductor polymer with electron-electron interactions. On the basis of this we further calculate the effect of the local lattice distortion on the exciton states and luminescent properties and find that the efficiency of luminescence is proportional to the strength of local lattice distortion under special electron-electron interaction parameters.

Numerical calculations of theB1gRaman spectrum of the two-dimensional Heisenberg model

The B1g Raman spectrum of the two-dimensional S=1/2 Heisenberg model is discussed within Loudon-Fleury theory at both zero and finite temperature. The exact T=0 spectrum for lattices with up to 6*6 sites is computed using Lanczos exact diagonalization. A quantum Monte Carlo (QMC) method is used to calculate the corresponding imaginary-time correlation function and its first two derivatives for lattices with up to 16*16 spins. The imaginary-time data is continued to real frequency using the maximum-entropy method, as well as a fit based on spinwave theory. The numerical results are compared with spinwave calculations for finite lattices. There is a surprisingly large change in the exact spectrum going from 4*4 to 6*6 sites. In the former case there is a single dominant two-magnon peak at frequency w/J appr. 3.0, whereas in the latter case there are two approximately equal-sized peaks at w/J appr. 2.7 and 3.9. This is in good qualitative agreement with the spinwave calculations including two-magnon processes on the same lattices. Both the Lanczos and the QMC results indicate that the actual infinite-size two-magnon profile is broader than the narrow peak obtained in spinwave theory, but the positions of the maxima agree to within a few percent. The higher-order contributions present in the numerical results are merged with the two-magnon profile and extend up to frequencies w/J appr. 7. The first three frequency cumulants of the spectrum are in excellent agreement with results previously obtained from a series expansion around the Ising limit. Typical experimental B1g$ spectra for La2CuO4 are only slightly broader than what we obtain here. The exchange constant extracted from the peak position is J appr. 1400K, in good agreement with values obtained from neutron scattering and NMR experiments.

Construction of size-consistent effective Hamiltonians

For a system consisting of two interacting subsystems, effective Hamiltonians for one subsystem are usually constructed by integrating out the degrees of freedom of the second subsystem. In contrast to usual treatments, our method for deriving effective Hamiltonians is based on the introduction of cumulants. Cumulants guarantee size consistency, a property that is not always evident in other approaches. The formalism applies for any temperature. Our method is based on a matrix formulation in the framework of a recently introduced cumulant-projection method. This method allows the treatment of strongly correlated systems, where conventional diagrammatic techniques are difficult to apply. The relation with perturbation theory is also shown. As a simple application we discuss the small polaron problem. Evaluating the one-electron dispersion relation in the strong-coupling case shows good agreement with recent results from exact Lanczos diagonalization. Our method has substantial advantages over perturbation theory.

Electron-phonon coupling in a one-band MX-chain model. A numerical study

We report and compare results on the ground state energy, renormalized phonon frequency, and optical conductivity of a one-band model for finite MX-chains at half-filling obtained within three types of methods: by exact Lanczos diagonalization, by factorizing the total wave function of the electron-phonon system (adiabatic ansatz), and within the analytical methods of the conventional many-body theory (mean-field, bubble approximation).

Motion of holes on the triangular lattice studied using the t-J model.

The motion of holes on the triangular lattice is studied using the t-J model. Within the Born self-consistent approximation and the exact Lanczos diagonalization, the single-hole physics is first analyzed. Then the spiral phase theory of Shraiman and Siggia is used to investigate the case of a finite density of holes. \textcopyright{} 1996 The American Physical Society.

The magnetic field behaviour of a Haldane-gap antiferromagnet

We investigate the magnetic field behaviour of an antiferromagnetic Heisenberg spin-1 chain with the most general single-ion anisotropy. We discuss the regime in which the magnetic field is below the transition value. The splitting of the Haldane triplet is obtained as a function of a field applied in an arbitrary orientation by means of a Lanczos exact diagonalization of chains of up to 16 spins. Our results are well summarized in terms of a first-order perturbation theory. We explain various level crossings that occur by the existence of discrete symmetries. A discussion is given of the electron-spin-resonance and neutron-scattering experiments on the compound Ni(C2H8N2)2NO2ClO4 (NENP).