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arXiv:cond-mat/0008068 · Physical review. B, Condensed matter

Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder

Matthias Vojta C, A. Hübsch, R. M. Noack

Published Jan 8, 2001• 51 citations
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Abstract

We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion $V$ using the density matrix renormalization-group technique. The ground state is homogeneous at small $V,$ a ``checkerboard'' charge-ordered insulator at large $V$ and not too small on site Coulomb repulsion U, and is phase separated for moderate or large $V$ and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling, charge-ordered regime that maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.

DOI
10.1103/physrevb.63.045105

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We investigate the charge-order transition at zero temperature in a two-leg Hubbard ladder with additional nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization group technique. We consider electron densities between quarter and half filling. For quarter filling and U=8t,U=8t,U=8t, we find evidence for a continuous phase transition between a homogeneous state at small VVV and a broken-symmetry state with ``checkerboard'' [wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$] charge order at large V.V.V. This transition to a checkerboard charge-ordered state remains present at all larger fillings, but becomes discontinuous at sufficiently large filling. We discuss the influence of U/tU/tU/t on the transition and estimate the position of the tricritical points.
We consider two aspects of the ground state of the $U=\ensuremath{\infty}$ Hubbard ladder: ferromagnetism and the metal-insulator transition at quarter-filling. First, we present rigorous results for the $U=\ensuremath{\infty}$ Hubbard ladder in the limit of the large interchain hopping ${(t}_{\ensuremath{\perp}}/t\ensuremath{\rightarrow}\ensuremath{\infty})$. In this limit, the total spin SSS of the ground state is shown to be zero for the electron density n< 0.5n<~0.5n< 0.5 and its maximum (S=Smax){(S=S}_{\mathrm{max}})(S=Smax​) for n>0.5n>0.5n>0.5. The charge gap at quarter-filling is ${2t}_{\ensuremath{\perp}}.$ We extend these results to finite ${t}_{\ensuremath{\perp}}/t$ by means of the density-matrix renormalization group method. We estimate the phase boundaries with respect to spontaneous magnetization and the charge gap at quarter-filling for finite ${t}_{\ensuremath{\perp}}/t$. Applying the extended Aharonov-Bohm method, we give numerical evidence that the critical ratio ${t}_{\ensuremath{\perp}}/t$, above which the charge gap opens, is less than 0.001. Ferromagnetism in the ttt-JJJ ladder is briefly discussed.
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.
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