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Acta Physica Polonica A

Electron Orderings of Half-Filled Extended Hubbard Models with Spin- and Charge-Exchange Interaction

W.R. Czart, S. Robaszkiewicz

Published Apr 1, 2006• 12 citations
Publisher

Abstract

The electron orderings of the half-filled extended Hubbard models (i) with anisotropic spin-exchange interactions (the t-U -J -J ⊥ model) and (ii) with charge-exchange interaction (the t-U -I model) are discussed.In particular, we present new results concerning the phase diagrams of the model (i) in the case of uniaxial spin exchange (J = 0) for d-dimensional hypercubic lattices (1 ≤ d ≤ ∞) and conclude about the basic effects of the particular spin-and charge-exchange interaction terms (J , J ⊥ , and I) in both models.

DOI
10.12693/aphyspola.109.577

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The electron orderings of the half-filled extended Hubbard models (i) with anisotropic spin-exchange interactions (the t-U -J -J ⊥ model) and (ii) with charge-exchange interaction (the t-U -I model) are discussed.In particular, we present new results concerning the phase diagrams of the model (i) in the case of uniaxial spin exchange (J = 0) for d-dimensional hypercubic lattices (1 ≤ d ≤ ∞) and conclude about the basic effects of the particular spin-and charge-exchange interaction terms (J , J ⊥ , and I) in both models.
The phase diagrams and electron orderings of the half-filled extended Hubbard models with anisotropic spin-exchange interactions (J⊥, J||) are studied. The cases of ferromagnetic (Jα 0) exchange couplings are considered for repulsive on-site interaction (U ≥ 0). The analysis of these t–U–J||–J⊥ models is performed for d-dimensional hypercubic lattices including d = 1 and d = ∞ by means of the (broken symmetry) HFA supplemented, for d = ∞, by the slave-boson mean-field method. The basic features of the derived phase diagrams are discussed.
The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.
In this paper, we study analytically a one-dimensional half-filled Hubbard model with nearest-neighbor Coulomb repulsion (V) and anisotropic spin exchange (J⊥ ≠ Jz) via the bosonization and renormalization-group (RG) techniques, and establish the rich phase diagrams based on the charge-spin separation hypothesis in the weak-coupling regime. The spin exchange anisotropy induces a non-critical behavior of spin correlations. The result indicates that the spin exchange anisotropy has an important impact on the topological phase diagram of the 1D extended Hubbard model.
Abstract We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.
Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.
In order to explore how superconductivity arises when charge fluctuations and spin fluctuations coexist, we have obtained a phase diagram against the off-site repulsion VVV and band filling nnn for the extended, repulsive Hubbard model on the square lattice with the fluctuation exchange approximation. We have found the existence of (i) a transition between dxy{d}_{xy}dxy​ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing symmetries, (ii) fff-pairing in between the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and CDW phases for intermediate 0.5<n<1.00.5<n<1.00.5<n<1.0 and large VVV, and (iii) for anisotropic cases the pairing symmetry changing, in agreement with a previously proposed ``generic phase diagram,'' as $d\ensuremath{\rightarrow}f\ensuremath{\rightarrow}s$ when VVV (hence the charge fluctuations) are increased. All these are consequences of the structure in the charge and spin susceptibilities, which have peaks habitating at common or segregated positions in kkk space.