One-particle irreducible density matrix for the spin disordered infinite $U$ Hubbard chain

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site $U$ interaction and intersite (ii) density-density interaction $W$ and (iii) Ising-like magnetic exchange interaction $J$ (between the nearest-neighbors). We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D-chain in two particular cases: (a) $W=0$ and $n=1$; (b) $U\rightarrow+\infty$ and $n=1/2$ ($W\neq 0$, $J\neq 0$)....

The electronic system of the 1D Hubbard model is not stable due to Peierls instability; the correlations are strong even for the weak Coulomb interaction. The resulting strongly correlated state without Landau quisi--particle excitations is known as the Luttinger liquid. Critical exponents of a power--law dependence of correlation functions at low energies differ substantially for the Luttinger and Fermi liquids. In this paper we evaluate two critical exponents that define no...

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 positive U to the limit of large interaction is also shown. This continuity property, when combined with the proof that the wavefunction obtained with the generalized Bethe Ansatz is normalizable, i...

Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and temperature-dependent correlation functions of the strongly interacting one-dimensional Hubbard model in the presence of an external trapping potential. These representations are exact and valid in both equilibrium and nonequilibrium scenarios like the on...

Paper: cond-mat/9311033 The Hubbard model of interacting electrons, like the Ising model of spin-spin interactions, is the simplest possible model displaying many ``real world'' features, but it is much more difficult to analyze qualitatively than the Ising model. After a third of a century of research, we are still not sure about many of its basic properties. This mini-review will explore what is known rigorously about the model and it will attempt to describe some open prob...

The local moment approach (LMA) has presented itself as a powerful semi-analytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group results. However, the most common correlated lattice model, the Hubbard model, has not been explored well wit...

We present an asymptotically exact solution of the $\infty-d$ Hubbard model at a special interaction strength $U_T$ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.

An interacting spin-fermion model is exactly solved on an open chain. In a certain representation, it is the nearest-neighbor Hubbard model in the limit of infinite $U$ (local interaction). Exact solution of its complete energy eigen-spectrum is accomplished by introducing a unitary transformation which maps the original problem to a tight-binding model of the fermions only. Physically, the exact solution implies the absence of Nagaoka ferromagnetism in the ground state for a...

A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy functional W, which is expressed as the sum of Hartree-Fock energy and the correlation energy E_C. Exact results are obtained for E_C of the Hubbard model on various periodic lattices. The functional dependence of E_C is analyzed by varying the ...

In this work, we study the wavefunctions of the one dimensional $1/r$ Hubbard model in the strong interaction limit $U =\infty$. A set of Gutzwiller-Jastorw wavefunctions are shown to be eigen-functions of the Hamiltonian. The entire excitation spectrum and the thermodynamics are also studied in terms of more generalized Jastrow wavefunctions. For the wavefunctions and integrability conditions at finite on-site energy, further investigations are needed.