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Journal of Physics Conference Series

Functional renormalization group approach for extended Hubbard model in a triangular lattice

Hirokazu Takashima, Sumio Ishihara

Published Sep 28, 2011• 0 citations
Publisher

Abstract

The extended Hubbard model in an anisotropic triangular lattice is analyzed at quarter filling by the functional renormalization group (fRG) approach. We obtain the finite temperature phase diagram in the plane of nearest inter-site Coulomb interaction Vp and next-nearest Coulomb interaction Vc. When Vp ? Vc, charge order does not occur down to the low temperature of 0.1tp, where the tp is the electron transfer between the nearest neighbor sites. We interpret the result using the random-phase approximation(RPA).

DOI
10.1088/1742-6596/320/1/012063

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The extended Hubbard model in an anisotropic triangular lattice is analyzed at quarter filling by the functional renormalization group (fRG) approach. We obtain the finite temperature phase diagram in the plane of nearest inter-site Coulomb interaction Vp and next-nearest Coulomb interaction Vc. When Vp ? Vc, charge order does not occur down to the low temperature of 0.1tp, where the tp is the electron transfer between the nearest neighbor sites. We interpret the result using the random-phase approximation(RPA).
We analyze the charge fluctuations in the two-dimensional quarter-filled extended Hubbard model on an anisotropic triangular lattice. We formulate the patch functional-renormalization-group method for this system and examine the full momentum dependence of the charge/spin susceptibilities. Two distinct peak structures in the charge susceptibility are obtained, where one is due to the Fermi-surface nesting condition and the other is due to the intersite Coulomb repulsions. It is shown that the mode-coupling effects within the particle-hole channel are crucial to improve the results of the random-phase-approximation, while the mode-coupling effects involving the particle-particle channel do not have strong effects. The validity of the random-phase-approximation is also discussed.
The extended Hubbard model in the atomic limit, which is equivalent to lattice S=1/2 fermionic gas, is considered on the triangular lattice. The model includes onsite Hubbard U interaction and both nearest-neighbor (W1) and next-nearest-neighbor (W2) density–density intersite interactions. The variational approach treating the U term exactly and the Wl terms in the mean-field approximation is used to investigate thermodynamics of the model and to find its finite temperature (T>0) phase diagrams (as a function of particle concentration) for W1>0 and W2<0. Two different types of charge-order (i.e., DCO and TCO phases) within 3×3 unit cells as well as the nonordered (NO) phase occur on the diagram. Moreover, several kinds of phase-separated (PS) states (NO/DCO, DCO/DCO, DCO/TCO, and TCO/TCO) are found to be stable for fixed concentration. Attractive W2<0 stabilizes PS states at T=0 and it extends the regions of their occurrence at T>0. The evolution of the diagrams with increasing of |W2|/W1 is investigated. It is found that some of the PS states are stable only at T>0. Two different critical values of |W2|/W1 are determined for the PS states, in which two ordered phases of the same type (i.e., two domains of the DCO or TCO phase) coexist.
Abstract Using a mean-field theory based upon Hartree—Fock approximation, we theoretically investigate the competition between the metallic conductivity, spin order and charge order phases in a two-dimensional half-filled extended Hubbard model on anisotropic triangular lattice. Bond order, double occupancy, spin and charge structure factor are calculated, and the phase diagram of the extended Hubbard model is presented. It is found that the interplay of strong interaction and geometric frustration leads to exotic phases, the charge fluctuation is enhanced and three kinds of charge orders appear with the introduction of the nearest-neighbor interaction. Moreover, for different frustrations, it is also found that the antiferromagnetic insulating phase and nonmagnetic insulating phase are rapidly suppressed, and eventually disappeared as the ratio between the nearest-neighbor interaction and on-site interaction increases. This indicates that spin order is also sensitive to the nearest-neighbor interaction. Finally, the single-site entanglement is calculated and it is found that a clear discontinuous of the single-site entanglement appears at the critical points of the phase transition.
Charge ordering is often found in the phase diagram of unconventional superconductors in close proximity to the superconducting state. This has led to the suggestion that fluctuations of charge order can mediate superconducting pairing. While several mechanisms can lead to charge order, one common mechanism is the long-range Coulomb interaction, resulting in a Wigner crystal charge ordered state. For an electron density of 0.5 per site, we investigate the extended Hubbard model on the two-dimensional square lattice using exact diagonalization and density matrix renormalization group methods. Our results show that the strength of pairing decreases with the nearest-neighbor Coulomb interaction strength VVV and remains weaker than the tendency of pairing for noninteracting electrons.