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arXiv:1001.5226 · Physical Review B

Phase separation and pairing regimes in the one-dimensional asymmetric Hubbard model

Luca Barbiero, Marco Casadei, Marcello Dalmonte, C. Degli Esposti Boschi, Elisa Ercolessi, F. Ortolani

Published Jun 15, 2010• 19 citations
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Abstract

We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries, respectively.

DOI
10.1103/physrevb.81.224512

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We address some open questions regarding the phase diagram of the one-dimensional Hubbard model with asymmetric hopping coefficients and balanced species. In the attractive regime we present a numerical study of the passage from on-site pairing dominant correlations at small asymmetries to charge-density waves in the region with markedly different hopping coefficients. In the repulsive regime we exploit two analytical treatments in the strong- and weak-coupling regimes in order to locate the onset of phase separation at small and large asymmetries, respectively.
The quantum phase transitions in the one-dimensional asymmetric Hubbard model are investigated with the bosonization approach. The conditions for the phase transition from density wave to phase separation, the correlation functions, and their exponents are obtained analytically. Our results show that the difference between the hopping integrals for up- and down-spin electrons is crucial for the occurrence of the phase separation. When the difference is large enough, the phase separation will appear even if the on-site interaction is small.
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 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 ${\mathrm{Ba}}_{1\ensuremath{-}x}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}.$
The ground-state phase diagram of the asymmetric Hubbard model is studied in one and two dimensions by a well-controlled numerical method. The method allows us to calculate directly the probabilities of particular phases in the approximate ground state and thus to specify the stability domains corresponding to phases with the highest probabilities. Depending on the electron filling nnn and the magnitude of the asymmetry tf∕td{t}_{f}∕{t}_{d}tf​∕td​ between the hopping integrals of fff and ddd electrons two different scenarios in formation of ground states are observed. At low electron fillings $(n\ensuremath{\leqslant}1∕3)$ the ground states are always phase segregated in the limit of strong asymmetry (td⪢tf)({t}_{d}⪢{t}_{f})(td​⪢tf​). With decreasing asymmetry the system undergoes a transition to the phase-separated state and then to the homogeneous state. For electron fillings n>1∕3n>1∕3n>1∕3 and weak Coulomb interactions the ground state is homogeneous for all values of asymmetry, while for intermediate and strong interactions the system exhibits the same sequence of phase transitions as for nnn small. Moreover, it is shown that the segregated phase is significantly stabilized with increasing electron filling, while the separated phases disappear gradually from the ground-state phase diagrams.
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.
Asymmetric two-leg Hubbard ladders with different on-site interactions Uy{U}_{y}Uy​ and hoppings ty{t}_{y}ty​ on each leg are investigated using the density-matrix renormalization group method and exact diagonalizations. The pairing found in symmetric ladders is robust against the introduction of the leg asymmetry. When studying pairing, one-band Hubbard ladder models are better described as one-dimensional correlated two-band models than as sublattices of higher-dimensional systems. The asymmetric Hubbard ladder provides us with a simple model for studying pairing in the crossover regime between charge-transfer and Mott insulators.