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Acta Physica Polonica A

Ground State Phase Diagram of the Extended Hubbard Model with Pair-Hopping Interaction in the Limit of Very Narrow Bandwidth

Konrad Jerzy Kapcia, W.R. Czart

Published Aug 1, 2016• 11 citations
Publisher

Abstract

The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing.We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions.The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.

DOI
10.12693/aphyspola.130.617

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The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing.We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions.The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.
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.
We study the extended Hubbard model with on-site density-density U and intersite pair hopping J interactions, i.e. the Penson-Kolb-Hubbard model.This report focuses mainly on the properties of the model at T ≥ 0 in the case of repulsive J (J < 0) which may stabilize superconductivity with η-pairing.The analysis is performed within the (broken symmetry) Hartree-Fock approximation for arbitrary interaction parameters (J < 0 and U ) and electron concentration (0 < n < 2) on the d = 2 square lattice.The phase diagrams of the model at T = 0 and at finite temperatures are examined taking into account magnetic and charge-ordered phases and superconducting states with η-and s-wave pairing.
We study the ground state phase diagrams of the extended Hubbard model with the pairhopping interaction J, i.e. the PensonKolbHubbard model.We concentrate on the case of attractive J (J > 0) which can stabilise s-wave pairing superconductivity in the system and competes with the on-site repulsive U .The evolution of the phase diagrams and order parameters for arbitrary electron density and representative values of the interaction parameters are analyzed within the (broken symmetry) HartreeFock approximation.The calculations are performed for the case of nearest-neighbors electron hopping t on the d = 2 square lattice.
Different kinds of instabilities (charge-density wave, spin-density wave, singlet superconductivity) in the one-dimensional Hubbard model with pair-hopping interaction are investigated using an approximate Bethe-Salpeter equation. The study is performed at any density of electrons and for arbitrary values of the model parameters. In the absence of the on-site interaction, no transition occurs at half-filling for any finite negative pair-hopping parameter, in agreement with recent results; our calculation suggests that the Penson-Kolb model (t,W) with \ensuremath{\Vert}W/t\ensuremath{\Vert}/sinkF{\mathit{k}}_{\mathit{F}}kF​ behaves qualitatively like the Hubbard model (t,U). Phase diagrams of the Penson-Kolb-Hubbard model (t,U,W) at various densities are presented. \textcopyright{} 1996 The American Physical Society.
In this work we study the ground state of the Penson-Kolb-Hubard model in the limit of narrow-bandwidth.We present phase diagrams of the model for fixed chemical potential and concentration (involving various phase separations).The results are derived within the Hartree-Fock approximation (HFA) in the narrow-bandwidth regime and compared with the exact ones in the atomic limit and the high-dimension regime.Our investigation reveals that the HFA can reconstruct the exact diagram at the ground state when the bandwidth approaches to zero.
The ground state of the one-dimensional half-filled Penson-Kolb-Hubbard model (with competing single-particle and pair hoppings in the presence of on-site Coulomb repulsion) has been investigated by a real space renormalization group method. The ground state energy, energy gap, local moment and several correlation functions are studied to obtain the phase diagram. The phase diagram consists of a spin density wave (SDW) state, a superconducting (SC) phase and a quasi-metallic phase dominated by short range SC correlations for positive values of the pair hopping amplitude; when this amplitude is negative, the phase diagram contains a near-metallic commensurate charge density wave and an SC phase of pairs with centre-of-mass momentum q= pi apart from an SDW phase.