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arXiv:cond-mat/9808253 · Physical review. B, Condensed matter

Weak-coupling phase diagram of the extended Hubbard model with correlated-hopping interaction

G. I. Japaridze, A. P. Kampf

Published May 15, 1999• 96 citations
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Abstract

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction ${T}^{*}$ 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.

DOI
10.1103/physrevb.59.12822

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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∗/\ensuremathπ{T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}T∗>0,∣U\ensuremath−2V∣<8T∗/\ensuremathπ and to a staggered magnetization located on bonds between sites for T∗<0,∣U\ensuremath−2V∣<8∣T∗∣/\ensuremathπ.{T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.T∗<0,∣U\ensuremath−2V∣<8∣T∗∣/\ensuremathπ. The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.
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.
At non-half-filling, a one-dimensional interacting electronic model (t–U–R) is studied analytically. The particular correlated hopping keeps particle–hole symmetry of the Hubbard model. Physically, the model involved is equivalent to an extended Hubbard chain incorporating a two-body (X) and a three-body (X˜) site-bond interactions with X˜=2X. The analysis of weak-coupling theory leads to the ground-state phase diagram, which consists of three types of metallic phases, characterized by the charge- (CDW) and spin-density-wave (SDW) and singlet-superconductivity (SS) instabilities.
Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.5 and first order for higher U.
We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g(g(g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for $U\ensuremath{\approx}2V$ in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential $\ensuremath{\Delta}$ or bond alternation $\ensuremath{\delta}.$ Although the alternating site potential $\ensuremath{\Delta}$ strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83,83,83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation $\ensuremath{\delta}$ destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with $\ensuremath{\delta}$ contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of $\ensuremath{\Delta}$ or $\ensuremath{\delta}$ changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.
The ground-state phase diagram of the one-dimensional Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper-pair center-of-mass momentum $Q=0 (\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase) and $Q=\ensuremath{\pi} ({\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator, and an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ and ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phases and the metallic Luttinger-liquid phase. The $\mathrm{BCS}\ensuremath{-}{\ensuremath{\eta}}_{0}$ phase exhibits a smooth crossover from a weak-coupling BCS type to a strong-coupling local-pair regime. The ${\ensuremath{\eta}}_{\ensuremath{\pi}}$ phase shows the properties of the doublon (zero-size Cooper-pair) superconductor with Cooper-pair center-of-mass momentum $Q=\ensuremath{\pi}.$ The transition into the ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-paired state corresponds to an abrupt change in the ground-state structure. After the transition the conduction band is completely destroyed and a new ${\ensuremath{\eta}}_{\ensuremath{\pi}}$-pair band, corresponding to the strongly correlated doublon motion, is created.
We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the weak-coupling renormalization-group approach ( g-ology) to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.