Simple method for exact calculation of thermodynamic properties of the 1D Hubbard model with infinite repulsion

It is shown that the canonical partition function in the 1D Hubbard model with U = ∞ in the nearest neighbor approximation is determined by the product of canonical partition functions of spinons and holons. In this approximation, the concentration and temperature dependences of the free and internal energies, as well as of the chemical potential, entropy, and heat capacity, are calculated for electron concentrations of 0 ≤ n _e < 1.     

Thermodynamic properties of the one-dimensional Hubbard model

We discuss the thermodynamic behaviour of the one-dimensional Hubbard model in the narrow-band regime, where the intra-atomic Coulomb-repulsion is large compared to the bandwidth. An approximation scheme on a perturbative basis is developed which applies for all temperatures. First order perturbation theory is performed for arbitrary electron densities; second order perturbation theory is discussed in the case of the half-filled band. Also the one-particle Green's function is calculated. Our approximation agrees excellently with numerical calculations. By comparison with exact results, which are available for some special limits, the range of validity of our approximation is estimated.     

Strong-coupling properties of the neutral Hubbard model

From a new variational approach to the Hubbard model, communicated previously [1], we derive the magnetic strong-coupling properties for the half filled band case of the Hubbard model in simple cubic lattices. The transition temperature from an AB-antiferromagnetic to a paramagnetic state, the sublattice magnetization and the localization of magnetic moments are investigated in detail. Near the strong coupling limit the results become asymptotically exact in a molecular field sense but they look reasonable even outside this asymptotic region.     

On the scaling limit of the 1D Hubbard model at half-filling

The dispersion relations and S-matrix of the one-dimensional Hubbard model at half-filling are onsidered in a certain scaling limit. (In the process we derive a useful small-coupling expansion of the exact lattice dispersion relations.) The resulting scattering theory is consistently identified as that of the SU(2) chiral-invariant Thirring (or Gross-Neveu) field theory, containing both massive and massless sectors.     

Zero finite-temperature charge stiffness within the half-filled 1D Hubbard model

Even though the one-dimensional (1D) Hubbard model is solvable by the Bethe ansatz, at half-filling its finite-temperature T>0$T>0$ transport properties remain poorly understood. In this paper we combine that solution with symmetry to show that within that prominent T=0$T=0$ 1D insulator the charge stiffness D(T)$D\left(T\right)$ vanishes for T>0$T>0$ and finite values of the on-site repulsion U$U$ in the thermodynamic limit. This result is exact and clarifies a long-standing open problem. It rules out that at half-filling the model is an ideal conductor in the thermodynamic limit. Whether at finite T$T$ and U>0$U>0$ it is an ideal insulator or a normal resistor remains an open question. That at half-filling the charge stiffness is finite at U=0$U=0$ and vanishes for U>0$U>0$ is found to result from a general transition from a conductor to an insulator or resistor occurring at U=U_c=0$U=U_c=0$ for all finite temperatures T>0$T>0$. (At T=0$T=0$ such a transition is the quantum metal to Mott-Hubbard-insulator transition.) The interplay of the η$\eta$-spin SU(2)$SU\left(2\right)$ symmetry with the hidden U(1)$U\left(1\right)$ symmetry beyond SO(4)$SO\left(4\right)$ is found to play a central role in the unusual finite-temperature charge transport properties of the 1D half-filled Hubbard model.     

Spectral properties of the attractive Hubbard model

We calculate the spectral functions, the band structure and the density of states of the 2D attractive Hubbard model in the intermediate coupling regime (i.e. the crossover regime between BCS theory and Bose-Einstein Condensation) using a grand canonical quantum Monte-Carlo approach and a maximum entropy procedure. The evolution of the spectral properties as a function of temperature is discussed. In particular, on lowering the temperature, we find a splitting of the single band present at high temperatures into several distinct branches, the number of which depends on the temperature. Received: 7 July 1998 / Accepted: 30 July 1998     

Superconducting properties of the attractive Hubbard model

A self-consistent set of equations for the one-electron self-energy in the ladder approximation is derived for the attractive Hubbard model in the superconducting state. The equations provide an extension of a T-matrix formalism recently used to study the effect of electron correlations on normal-state properties. An approximation to the set of equations is solved numerically in the intermediate coupling regime, and the one-particle spectral functions are found to have four peaks. This feature is traced back to a peak in the self-energy, which is related to the formation of real-space bound states. For comparison we extend the moment approach to the superconducting state and discuss the crossover from the weak (BCS) to the intermediate coupling regime from the perspective of single-particle spectral densities.     

Electronic state in the 2D Hubbard model

Electronic state of the 2D Hubbard model near the half-filling is analyzed by use of the composite operator method. Doping and temperature dependence of density of states show similar behaviors obtained in numerical simulation. The weight of the upper and lower Hubbard bands at the half filling are not evenly distributed in the Brillouin zone, keeping roughly the original band distribution. With hole doping the lower Hubbard band spreads in the whole zone.     

Two-particle states in the 2D Hubbard model

An exact solution is proposed for the problem of two singlet electrons (zero-spin bosons) interacting through a Hubbard-type potential on a bounded quadratic lattice. Exact two-particle states and the energy spectrum are constructed.     

The electronic spectrum and the metal-insulator transition in the Hubbard model

Calculations of quasiparticle spectra including high-order terms in the irreducible Green function method are presented. The metal-insulator transition of the 2.5-kind is connected with Fermi-surface collapse. In the band limit Fermi-liquid behaviour is obtained for the whole k-space except a small region near the Fermi surface where two quasibands exist which obey Gibbs statistics.     

Continuity properties of the electronic spectrum of 1D quasicrystals

In this paper we consider operatorsH(,x) defined onl ²() by

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     

Density matrix spectra and order parameters in the 1D extended Hubbard model

Without any knowledge of the symmetry existing in a system, we derive the exact forms of the order parameters which show long-range correlations in the ground state of the one-dimensional (1D) extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which could not be derived systematically via traditional methods in the condensed matter theory.     

Multifloquet to single electronic channel transition in the transport properties of a resistive 1D driven disordered ring

We investigate the dc response of a 1D disordered ring coupled to a reservoir and driven by a magnetic flux with a linear dependence on time. We identify two regimes: (i) A localized or large length L regime, characterized by a dc conductance, g(dc), whose probability distribution P(g(dc)) is identical to the one exhibited by a 1D wire of the same length L and disorder strength placed in a two terminal Landauer setup and (ii) a multifloquet regime for small L and weak coupling to the reservoir, which exhibits large currents and conductances that can be g(dc)>1, in spite of the fact that the ring contains spinless electrons and a single electronic transmission channel. The crossover length between the multifloquet to the single-channel transport regime Lc is controlled by the coupling to the reservoir.