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Properties of extended Hubbard models with anisotropic spin-exchange interaction

W.R. Czart, S. Robaszkiewicz

Published Jan 1, 2007• 1 citation
OpenAlex

Abstract

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.

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arXiv:2302.01062•Physica Scripta•May 4, 2023•3 citations
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 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 superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
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.
We discuss global structures of ground-state phase diagrams in a one-dimensional half-filled electron system with on-site and spin-dependent nearest-neighbor-site Coulomb interactions. We compare our numerical calculation data for phase boundary lines with their analytical expressions in three limiting regions of interaction parameters and find good agreement between them. In the intermediate-coupling region, however, we observe nontrivial structures of phase diagrams: For systems with weak easy-plain anisotropy, both the bond-located spin- and charge-density-wave phases are realized. The latter contacts with the ferromagnetic phase stabilized in the strong-coupling region. On the other hand, when anisotropy becomes large, the intermediate phase disappears and consequently a direct transition between the former and ferromagnetic phase is observed.
In this paper the two-dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble.Such an eective simple model could describe behavior of insulating (anti)ferromagnets.In the model considered the Coulomb interaction (U ) is on-site and the magnetic interactions in z-direction (J > 0, antiferromagnetic) are restricted to nearest-neighbors.Simulations of the model have been performed on a square lattice consisting of N = L × L = 400 sites (L = 20) in order to obtain the full phase diagram for U/(4J) = 1.Results obtained for on-site repulsion (U > 0) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence.We present a phase diagram as well as some thermodynamic properties of the model for the case of U/(4J) = 1 (and arbitrary chemical potential and arbitrary electron concentration).The AFNO transition can be second-order as well as rst-order and the tricritical point occurs on the diagram.
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.