RVB theory of the Hubbard model on the triangular lattice

We propose a Green's function technique, to investigate finite-temperature properties of the Hubbard model on the triangular lattice. The lattices are covered by dimers. The method is exact in two limits:U=0 or decoupled dimers. We apply this approximate method to calculate the ground state energy, the specific heat and the single-particle spectral weight for the 1/2-filled case. The largest lattice considered has 16×16 sites. The approximate ground state energy as a function of the on-site interactionU oscillates around the exact energyin the 1/2-filled case. We find two peaks in the specific heat. ForU5t the single-particle spectral weight splits into upper and lower Hubbard bandasymmetrically. Thus in the 1/2-filled case the chemical potential is placed in the upper band leading to a metallic state. The approximate technique yields a finite zero-point entropy for mediumU. All the investigations signal a RVB state in the range of mediumU as formerly proposed by Callaway.     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

Band effects on the conductivity for a two-band Hubbard model

The band effects on the conductivity of a one-dimensional two-band Hubbard model is studied based on the ground state energy analysis. It is found that the system with filling factor one is a metal at zero temperature if the on-site interaction U is smaller than a critical value U_c, and is an insulator if U is larger than U_c. The value of metal-insulator transition point U_c is obtained. This result is different from that of 1D single-band Hubbard model where the quantum phase transition point U_c=0. Therefore, the orbital degree of freedom plays an essential role in the states of matter.     

Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit

In this work, we present a proof of the existence of real and ordered solutions to the generalized Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U>0 to U=∞ is also shown. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. Lastly, for the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.     

Quantum spin liquid near Mott transition with fermionized π-vortices

In this paper, we study the non-magnetic insulator state near Mott transition of 2D π-flux Hubbard model on square lattice and find that such non-magnetic insulator state is quantum spin liquid state with nodal fermionic excitations – nodal spin liquid (NSL). When there exists small easy-plane anisotropic energy, the ground state becomes Z ₂ topological spin liquid (TSL) with full gapped excitations. The U(1) × U(1) mutual-Chern-Simons (MCS) theory is obtained to describe the low energy physics of NSL and TSL.     

Electron correlations in the effective Hubbard model

A new general unitary transformation is obtained, which allows to get in a controllable manner the effective Hamiltonian of the Hubbard model at an arbitrary sign and value of the intraatomic constantU and for any given filling number of electrons per atomn. It is shown that atU<0 the effective Hamiltonian has a multipseudospin exchange form for an arbitrary filling and there exist hidden localSU(2) andU(1) gauge symmetries in the restricted Hilbert space.     

On the ground state of the half-filled Hubbard model

We calculate the ground state of the half-filled Hubbard model and its energy by starting from a spindensity wave approximation and improving it by incorporating transverse spin fluctuations. The calculations are done by employing a projection method. The quality of the proposed approximation is particularly high for intermediate and large Coulomb repulsionU, where it exceeds considerably e.g. that of the Gutzwiller projected spin-density wave state. To ordert ²/U (wheret is the hopping matrix element), our approximation is shown to be equivalent to a recent Coupled Cluster calculation for the Heisenberg antiferromagnet. Finally we show how to ordert ²/U the linear spin-wave approximation for the Heisenberg antiferromagnet may be obtained.     

Excitation spectrum of one-dimensional extended ionic Hubbard model

We use perturbative continuous unitary transformations (PCUT) to study the one dimensional extended ionic Hubbard model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, V. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system; (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V = 0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of V there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion U is to split singlet and triplet collective excitation branches, while V tends to pull the singlet branches below the continuum to make them bound states.     

CNDO/S-CI calculation of Hubbard parameters for doubly charged TCNQ tetramer

Using the CNDO/S-CI method the energies of the low-lying singlets and triplets of a doubly charged tetramer of TCNQ in the eclipsed geometry were calculated. The exact solution of the nearest-neighbour-version of the EHH for the case of two electrons and four sites was found. Fitting the EHH energy levels on the CNDO/S-CI spectra, the Hubbard parameters were estimated:U ₀=2.50 eV,V ₁=0.71 eV, ¦t¦=0.32 eV. The effect of strong correlation of the unpaired electrons on the electronic distribution in the ground and optically excited states of the tetramer is discussed.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Antiferromagnetism in the Hubbard model

The energy spectrum of the two-sublattice Hubbard model is obtained in the static-fluctuation approximation. It is shown how the structure of the energy spectrum is modified as the parameters of the Hubbard model are varied. The ground state of the simple Hubbard model of dimension d=2 is the dielectric antiferromagnetic state. The author derives a consistency equation for the magnetization, which has an antiferromagnetic solution. Fiz. Tverd. Tela (St. Petersburg) 39, 1594–1599 (September 1997)     

The singlet state in the Hubbard model with U=∞

We discuss, in connection with the problem of the ground state in the Hubbard model with U=∞, the normal (nonmagnetic) N-state of a system over the entire range of electron concentrations n≤1. It is found that in a one-particle approximation, e.g., in the generalized Hartree-Fock approximation, the energy ε ₀(n) of the N-state is lower than the energy ε _FM(n) of a saturated ferromagnetic state for all values of n. Using the random phase approximation we calculate the dynamical magnetic susceptibility and show that the N-state is stable for all values of n. A formally exact representation is derived for the mass operator of the one-particle electron Green’s function, and its expression in the self-consistent Born approximation is obtained. We discuss the first Born approximation and show that when correlations are taken into account, the attenuation vanishes on the Fermi surface and the electron distribution function at T=0 acquires a Migdal discontinuity, whose magnitude depends on n. The energy of the N-state in this approximation is still lower than ε _FM(n) for n<1. We show that the spin correlation functions are isotropic, which is a characteristic feature of the singlet states of the system. We calculate the spin correlation function for the nearest neighbors in the zeroth approximation as a function of n. Finally, we conclude that the singlet state of the system in the thermodynamic limit is the ground state. Zh. éksp. Teor. Fiz. 114, 2130–2144 (December 1998)     

Non-adiabatic electron-phonon coupling in the two-sites two-electrons system

The electronic and ibrational properies of a system of two electrons or excitons at two sites are investgated in a simple model combining the ideas of the Hubbard and Holstein Hamiltonans. We analyse the competition of the interactions which enter this model as parameers for the transfer energyT, the (on-site) Coulomb energyU, the short-range electron-phonon coupling, represented by the stabilization energyS and the vibrational energy (). For the whole range of these parameters the spectrum of the 50 lowest eigenstates has been numerically determined. As in the adiabatic approximation (=0) the ground state suffers a structural change due to a charge transfer instability, ifS is sufficiently large. In the case of finite this transition to a distorted state is no longer sharply defined by a criticalS. With regard to the lowest excited states the electronic system can be described by the adiabatic ground state for smallS as well as for largeS. Correspondingly the eigenfunctions of undisplaced or displaced harmonic oscillators, respectively, yield the lattice dynamics. In the range of intermediateS the situation is more complicated. Here the relation between the eigenfunctions and the adiabatic potentials as well as the appearance of metastable states and their connection to the charge transfer is discussed at some length.     

Some exact results for the Kondo lattice with infinite exchange interaction

Using an exact equivalence between the Kondo lattice with infinite J and the Hubbard model with infinite U, we show that the ground state of the Kondo lattice is non-magnetic for concentrations of conduction electrons close to 1, but there are still some magnetic regions even for J → ∞.     

Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.     

Magnetic and non-magnetic ground states of the Kondo lattice

We use the variational method to investigate the ground state phase diagram of the Kondo lattice Hamiltonian for arbitraryJ/W, and conduction electron concentrationn _c (J is the Kondo coupling andW the bandwidth). We are particularly interested in the question under which circumstances the globally singlet (collective Kondo) Fermi liquid type ground state becomes unstable against magnetic ordering. For the collective Kondo singlet we use the lattice generalization of Yosida's wavefunction which implies the existence of a large Fermi volume, in accordance with Luttinger's theorem. Using the Gutzwiller approximation, we derive closed-form results for the ground state energy at arbitraryJ/W andn _c, and for the Kondo gap atn _c=1. We introduce simple trial states to describe ferromagnetic, antiferromagnetic, and spiral ordering in the small-J (RKKY) regime, and Nagaoka type ferromagnetism at largeJ/W. We study three particular cases: a band with a constant density of states, and the (tight binding) linear chain, and square lattice periodic Kondo models. We find that the lattice enhancement of the Kondo effect, which is described in our theory of the Fermi liquid state, pushes the RKKY-to-nonmagnetic phase boundary to much smaller values ofJ/W than it was previously thought. In our study of the square lattice case, we also find a region of itinerant, Nagaoka-type ferromagnetism at largeJ/W forn _c 1/3.     

Strong-coupling thermodynamics of the Hubbard model

Thermodynamic properties of the half-filled-band Hubbard model are calculated in the strong-coupling regime for a simple cubic structure, using the Bogoliubov variational principle. When the Coulomb-interactionV _o exceeds the bandwidthJ, we find a phase transition from a condensed phase of itinerant electrons into a state of localized ones at a transition temperature which exhibits the asymptotic behaviourT ₀J ²/V ₀ at largeV ₀.     

Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

Filling dependence of correlation exponents and metal-Mott insulator transition in strongly correlated electron systems

Using a universal relation between electron filling factor and ground state energy,this paper studies the dependence of correlation exponents on the electron filling factor of one-dimensional extended Hubbard model in a strong coupling regime,and demonstrates that in contrast to the usual Hubbard model(gc = 1/2),the dimensionless coupling strength parameter g c heavily depends on the electron filling,and it has a "particle-hole" symmetry about electron quarter filling point.As increasing the nearest neighbouring repulsive interaction,the single particle spectral weight is transferred from low energy to high energy regimes.Moreover,at electron quarter filling,there is a metal-Mott insulator transition at the strong coupling point gc = 1/4,and this transition is a continuous phase transition.