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arXiv:cond-mat/9705067 · Journal of the Physical Society of Japan

Quantum Monte Carlo Study of an Extended Hubbard Model on a Two-Leg Ladder

Tomo Munehisa, Yasuko Munehisa

Published Dec 15, 1997• 4 citations
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Abstract

An extended Hubbard model on a two-leg ladder is numerically studied by means of the quantum Monte Carlo techniques. The model we study has the nearest-neighbor interactions which are repulsive along chains and attractive for rungs. The plots of the doping parameter versus the chemical potential show two cliff-like regions and a large plateau region. Results on the charge susceptibility suggest it diverges in these cliff-like regions. These observations might imply a signal to the phase separation, which should be related to the effective attractive interactions along chains.

DOI
10.1143/jpsj.66.3876

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An extended Hubbard model on a two-leg ladder is numerically studied by means of the quantum Monte Carlo techniques. The model we study has the nearest-neighbor interactions which are repulsive along chains and attractive for rungs. The plots of the doping parameter versus the chemical potential show two cliff-like regions and a large plateau region. Results on the charge susceptibility suggest it diverges in these cliff-like regions. These observations might imply a signal to the phase separation, which should be related to the effective attractive interactions along chains.
We present quantum Monte Carlo results for the Hubbard model on a ladder using the re-structuring method which employ eigenstates of two-site system on a rung to construct a complete set. From technical reasons we concentrate on the case in which the hopping along the leg is much less than the hopping on the rung. We observe the ground state of the half-filled system is made of singlet-like states described in this paper and its first excited state contains one triplet rung. When the system is lightly doped states composed of an electron and a hole appear on some rungs. We find very few hole-pairing on the rung upon doping up to the quarter-filled case.
We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion VVV using the density matrix renormalization-group technique. The ground state is homogeneous at small V,V,V, a ``checkerboard'' charge-ordered insulator at large VVV and not too small on site Coulomb repulsion U, and is phase separated for moderate or large VVV 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.
The Hubbard Hamiltonian on a two-leg ladder is studied numerically using quantum Monte Carlo and Exact Diagonalization techniques. A rung interaction, VVV, is turned on such that the resulting model has an exact SO(5) symmetry when V=−UV=-UV=−U. The evolution of the low energy excitation spectrum is presented from the pure Hubbard ladder to the SO(5) ladder. It is shown that the low energy excitations in the pure Hubbard ladder have an approximate SO(5) symmetry.
In this paper the two-dimensional extended Hubbard model with intersite magnetic Ising-like interaction in the atomic limit is analyzed by means of the classical Monte Carlo method in the grand canonical ensemble.Such an eective simple model could describe behavior of insulating (anti)ferromagnets.In the model considered the Coulomb interaction (U ) is on-site and the magnetic interactions in z-direction (J > 0, antiferromagnetic) are restricted to nearest-neighbors.Simulations of the model have been performed on a square lattice consisting of N = L × L = 400 sites (L = 20) in order to obtain the full phase diagram for U/(4J) = 1.Results obtained for on-site repulsion (U > 0) show that, apart from homogeneous non-ordered (NO) and ordered magnetic (antiferromagnetic, AF) phases, there is also a region of phase separation (PS: AF/NO) occurrence.We present a phase diagram as well as some thermodynamic properties of the model for the case of U/(4J) = 1 (and arbitrary chemical potential and arbitrary electron concentration).The AFNO transition can be second-order as well as rst-order and the tricritical point occurs on the diagram.
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.