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Journal of Physics Condensed Matter

Bond-located ordering in the one-dimensional Penson - Kolb - Hubbard model

G. I. Japaridze, E. Müller‐Hartmann

Published Nov 24, 1997• 28 citations
Publisher

Abstract

In this paper we study the ground-state phase diagram of the one-dimensional half-filled repulsive (U > 0) Hubbard model supplemented with the pair-hopping interaction (W) (the Penson - Kolb - Hubbard model) using the continuum-limit field theory approach. We compare the low-energy properties of the U > 0 Hubbard model and W > 0 Penson - Kolb model. We show that, despite similar excitation spectra, the character of instabilities in these models is completely different. In contrast to the Hubbard model, in the case of the Penson - Kolb model, the dynamical generation of a charge gap leads to the suppression of spin-density-wave (SDW) fluctuations. The charge-density-wave fluctuations survive and coexist with bond-located SDW (Bd-SDW) instabilities. The Bd-SDW corresponds to a magnetically ordered state with staggered magnetization located on bonds between sites. The possibility of bond-located ordering is connected with the site-off-diagonal nature of the pair-hopping interaction. In the case of PKH the bond-ordered states exist at . For W > U/2 the Bd-SDW is realized while for the dimerized phase is realized.

DOI
10.1088/0953-8984/9/47/018

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In this paper we study the ground-state phase diagram of the one-dimensional half-filled repulsive (U > 0) Hubbard model supplemented with the pair-hopping interaction (W) (the Penson - Kolb - Hubbard model) using the continuum-limit field theory approach. We compare the low-energy properties of the U > 0 Hubbard model and W > 0 Penson - Kolb model. We show that, despite similar excitation spectra, the character of instabilities in these models is completely different. In contrast to the Hubbard model, in the case of the Penson - Kolb model, the dynamical generation of a charge gap leads to the suppression of spin-density-wave (SDW) fluctuations. The charge-density-wave fluctuations survive and coexist with bond-located SDW (Bd-SDW) instabilities. The Bd-SDW corresponds to a magnetically ordered state with staggered magnetization located on bonds between sites. The possibility of bond-located ordering is connected with the site-off-diagonal nature of the pair-hopping interaction. In the case of PKH the bond-ordered states exist at . For W > U/2 the Bd-SDW is realized while for the dimerized phase is realized.
A one-dimensional model of interacting electrons with on-site U, nearest- neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, \U - 2V\ < \2W\ and a bond-spin-density-wave (BSDW) for W > 0, \U - 2V\ < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the eta(pi) -superconducting phase at \U - 2V\ much less than 2t less than or equal to W is briefly discussed.
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.
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.
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 effects of a bond-charge interaction (or correlated hopping) on the properties of the extended [i.e., with both on-site (U) and nearest-neighbor (V) repulsions] Hubbard model in one dimension at half-filling. Energy gaps and correlation functions are calculated by Lanczos diagonalization on finite systems. We find that, irrespective of the sign of the bond-charge interaction, X, the charge-density-wave (CDW) state is more robust than the spin-density-wave (SDW) state. A small bond-charge interaction term is enough to make the differences between the CDW and SDW correlation functions much less dramatic than when X=0. For X=t and fixed V2t (t is the uncorrelated hopping integral), there is an intermediate phase between a charge ordered phase and a phase corresponding to singly occupied sites, the nature of which we clarify: it is characterized by a succession of critical points, each of which corresponds to a different density of doubly occupied sites. We also find an unusual slowly decaying staggered spin-density correlation function, which is suggestive of some degree of ordering. No enhancement of pairing correlations was found for any X in the range examined. \textcopyright{} 1996 The American Physical Society.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction T∗{T}^{*}T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.