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Physical review. B, Condensed matter

Phase diagram of the extended attractive Hubbard model in one dimension

Kazuhiko Kuroki, Koichi Kusakabe, Hideo Aoki

Published Jul 1, 1994• 21 citations
Publisher

Abstract

Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.

DOI
10.1103/physrevb.50.575

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Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.
We investigated the one-dimensional extended Hubbard model with the on-site interaction U and the nearest-neighbor interaction V by using the numerical diagonalization method. Assuming the Luttinger liquid relations, we obtained the phase diagram of the ground state on the U - V plane. In the weak coupling region, the phase diagram agrees with the result of g -ology. On the other hand, in the strong coupling region for V ≫∣ t ∣, a novel superconducting phase appears both for positive and negative U . We also investigated the charge gap and the spin gap. The results suggest that the superconducting phase extends over the Tomonaga-Luttinger region (without spin gap) and the Luther-Emery region (with spin gap).
We consider the extended Hubbard model with attractive on-site interaction U and nearest-neighbor repulsions V. We construct an effective Hamiltonian Heff{H}_{\mathrm{eff}}Heff​ for hopping $t\ensuremath{\ll}V$ and arbitrary U<0.U<0.U<0. Retaining the most important terms, Heff{H}_{\mathrm{eff}}Heff​ can be mapped onto two XXZ\mathrm{XXZ}XXZ models, solved by the Bethe ansatz. The quantum phase diagram shows two Luttinger liquid phases and a region of phase separation between them. For density n<0.422n<0.422n<0.422 and $U<\ensuremath{-}4,$ singlet superconducting correlations dominate at large distances. For some parameters, the results are in qualitative agreement with experiments in ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}.$
We study the phase diagram of the one-dimensional U-V model at quarter filling in the most general case where the on-site and first-neighbor interactions U and V can be both attractive and repulsive. The results have been obtained using exact diagonalization of small clusters and variational techniques, as well as exact results in various limits. We have analyzed four properties of the ground state: (i) whether it is insulating or metallic; (ii) whether it is homogeneous or phase separated; (iii) whether it has a spin gap; (iv) whether it has dominant superconducting fluctuations. With eight phases, the resulting phase diagram is unexpectedly rich. The four phases not found in the weak coupling limit are: (i) an insulating phase when U and V are large enough; (ii) a region of phase separation when V is attractive; (iii) another region of phase separation when V is large enough and U small; (iv) a region with dominant superconducting fluctuations when V is intermediate and U small. The actual nature of this last plase, which has pairs but no spin gap, is not fully clear yet.
The extended Hubbard model in one dimension is studied for half-filled bands using a continuum theory based on the Luttinger model. Interactions going beyond the Luttinger model are treated with a renormalization group. We compute correlation functions and use these to establish the phase diagram of the model. It compares favorably with earlier numerical work. Specifically, we identify additional interaction terms coupling charge and spin degrees of freedom; one of them is shown to mediate the crossover from a continuous to a first-order transition from spin- to charge-density waves at a finite value of U=2V. Our approach suggests viewing the model on this line as two weakly coupled interpenetrating systems of up-spin and down-spin electrons with strong backscattering interactions favoring charge-density waves separately in each of the subsystems. A first-order transition occurring for attractive interactions is interpreted as a characteristic instability of the Luttinger liquid towards phase separation. We finally discuss a possible equivalence to some recent studies of coupled two-dimensional XY models.
We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on-site interaction U and a nearest-neighbor interaction V. We focus on the ground state phases of the model in the $V\ensuremath{\gg}U$ region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=VPS.{V=V}_{\mathrm{PS}}.V=VPS​. Using quantum Monte Carlo methods on lattices much larger than in previous Lancz\"os diagonalization studies, we determine the boundary of phase separation, the Luttinger-liquid correlation exponent ${K}_{\ensuremath{\rho}},$ and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state reenters from phase separation as the electron density is increased towards half filling. For V<VPS,V<{V}_{\mathrm{PS}},V<VPS​, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger liquid with ${K}_{\ensuremath{\rho}}<1,$ but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger liquid.
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.