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Physical review. B, Condensed matter

Ground-state phase diagram of an extended Hubbard chain with correlated hopping at half-filling

Liliana Arrachea, Eduardo R. Gagliano, Armando A. Aligia

Published Jan 1, 1997• 40 citations
Publisher

Abstract

We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin \ensuremath{\sigma}, which depends on the sum of particles ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$ with opposite spin in the two sites involved. The hopping matrix elements are denoted by ${\mathrm{t}}_{\mathrm{AA}}$,${\mathrm{t}}_{\mathrm{AB}}$,${\mathrm{t}}_{\mathrm{BB}}$ for ${\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}$=0,1,2, respectively. For 0${\mathrm{t}}_{\mathrm{AB}}$${\mathrm{t}}_{\mathrm{AA}}$=${\mathrm{t}}_{\mathrm{BB}}$, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of ${\mathrm{t}}_{\mathrm{AB}}$=0. For 0${\mathrm{t}}_{\mathrm{AB}}$${\mathrm{t}}_{\mathrm{AA}}$=${\mathrm{t}}_{\mathrm{BB}}$, the GS is a M for sufficiently low values of U and V. In contrast, when ${\mathrm{t}}_{\mathrm{AA}}$+${\mathrm{t}}_{\mathrm{BB}}$-${2\mathrm{t}}_{\mathrm{AB}}$=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.

DOI
10.1103/physrevb.55.1173

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We consider a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and nearest-neighbor hopping for spin \ensuremath{\sigma}, which depends on the sum of particles m\ensuremathσ\ensuremath−∣Am{\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}m\ensuremathσ\ensuremath−∣Am​ with opposite spin in the two sites involved. The hopping matrix elements are denoted by tAA{\mathrm{t}}_{\mathrm{AA}}tAA​,tAB{\mathrm{t}}_{\mathrm{AB}}tAB​,tBB{\mathrm{t}}_{\mathrm{BB}}tBB​ for m\ensuremathσ\ensuremath−∣Am{\mathrm{m}}_{\mathrm{\ensuremath{\sigma}}\ensuremath{-}|\mathrm{A}\mathrm{m}}m\ensuremathσ\ensuremath−∣Am​=0,1,2, respectively. For 0{\mathrm{t}}_{\mathrm{AB}}$${\mathrm{t}}_{\mathrm{AA}}=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, we have determined the regions of parameters for which the ground-state (GS) of the one-dimensional system is a charge-density wave (CDW), a spin-density wave (SDW), or a metal (M), using Hartree-Fock, exact diagonalization of finite chains and quantum Monte Carlo. The results agree qualitatively with the exactly solvable limit of tAB{\mathrm{t}}_{\mathrm{AB}}tAB​=0. For 0{\mathrm{t}}_{\mathrm{AB}}$${\mathrm{t}}_{\mathrm{AA}}=tBB{\mathrm{t}}_{\mathrm{BB}}tBB​, the GS is a M for sufficiently low values of U and V. In contrast, when tAA{\mathrm{t}}_{\mathrm{AA}}tAA​+tBB{\mathrm{t}}_{\mathrm{BB}}tBB​-2tAB{2\mathrm{t}}_{\mathrm{AB}}2tAB​=0, our results suggest that the GS is either a CDW or a SDW, with the boundary between them lying near the line U=2V.
We study a generalized Hubbard model with on-site interaction U, nearest-neighbor repulsion V, and general correlated hopping under the condition that the number of doubly occupied sites is conserved. We find the exact ground state (GS) in arbitrary dimension in two wide regions of parameters. In one of them the GS is a Mott insulator (MI) and in the other it is a charge-density wave (CDW). The boundary of the MI and a large part of that of the CDW are determined exactly for relevant lattices. We study numerically the effect of relaxing the above-mentioned condition.
We consider an extended Hubbard model of interacting fermions on a lattice. The fermion kinetic energy corresponds to a tight-binding Hamiltonian with nearest-neighbor (-t) and next-nearest-neighbor (t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH) hopping matrix elements. In addition to the on-site Hubbard interaction (U) we also consider a nearest-neighbor repulsion (V). We obtain the zero-temperature phase diagram of our model within the Hartree-Fock approximation. We consider ground states having charge- and spin-density-wave ordering as well as states with orbital antiferromagnetism or spin nematic order. The latter two states correspond to particle-hole binding with ${\mathrm{d}}_{{\mathrm{x}}^{2}\mathrm{\ensuremath{-}}{\mathrm{y}}^{2}}$ symmetry in the charge and spin channels, respectively. For t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH=0, only the charge-density-wave and spin-density-wave states are energetically stable. For nonzero t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH, we find that orbital antiferromagnetism (or spin nematic) order is stable over a finite portion of the phase diagram at weak coupling. This region of stability is seen to grow with increasing values of t∣IH{\mathrm{t}}^{|\mathrm{I}\mathrm{H}}t∣IH.
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.
We determine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site (nearest-neighbor) repulsive interaction U (V) and nearest-neighbor hopping t using the density-matrix renormalization group technique. Based on the results of the excitation gaps, Luttinger-liquid exponents, and bond-order-wave (BOW) order parameter, we confirm that the BOW phase appears in a substantial region between the charge-density-wave (CDW) and spin-density-wave phases. Each phase boundary is determined by multiple means and it allows us to make a cross-check on the validity of our estimations. We also find that the BOW-CDW transition changes from continuous to first order at the tricritical point (U(t),V(t)) approximately (5.89 t,3.10 t) and the BOW phase shrinks to zero at the critical end point (U(c),V(c)) approximately (9.25 t,4.76 t).
We investigate the ground-state phase diagram of the half-filled one-dimensional Hubbard model with next-nearest-neighbor hopping using the density-matrix renormalization-group technique as well as an unrestricted Hartree-Fock approximation. We find commensurate and incommensurate disordered magnetic insulating phases and a spin-gapped metallic phase in addition to the one-dimensional Heisenberg phase. At large on-site Coulomb repulsion U, we make contact with the phase diagram of the frustrated Heisenberg chain, which has spin-gapped phases for sufficiently large frustration. For weak U, sufficiently large next-nearest-neighbor hopping t2{t}_{2}t2​ leads to a band structure with four Fermi points rather than two, producing a spin-gapped metallic phase. As U is increased in this regime, the system undergoes a Mott-Hubbard transition to a frustrated antiferromagnetic insulator.
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.