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The ground state phase diagram of the 1D Hubbard chain with pair-hopping interaction is studied. The analysis of the model is performed using the continuum-limit field theory approach and exact diagonalization studies. At half-filling the phase diagram is shown to consist of two superconducting states with Cooper pair center-of-mass momentum Q=0 (BCS-eta_0 phase) and Q=pi (eta_pi-phase) and four insulating phases corresponding to the Mott antiferromagnet, the Peierls dimerized phase, the charge-density-wave (CDW) insulator as well as an unconventional insulating phase characterized by the coexistence of a CDW and a bond-located staggered magnetization. Away from half-filling the phase diagram consists of the superconducting BCS-eta_0 and eta_pi phases and the metallic Luttinger-liquid phase. The BCS-eta_0 phase exhibits smooth crossover from a weak-coupling BCS type to a strong coupling local-pair regime. The eta_pi phase shows properties of the doublon (zero size Cooper pair) superconductor with Cooper pair center-of-mass momentum Q=pi. The transition into the eta_pi- paired state corresponds to an abrupt change in the groundstate structure. After the transition the conduction band is completely destroyed and a new eta_pi-pair band corresponding to the strongly correlated doublon motion is created.
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Hubbard ladders are an important stepping stone to the physics of the two-dimensional Hubbard model. While many of their properties are accessible to numerical and analytical techniques, the question of whether weakly hole-doped Hubbard ladders are dominated by superconducting or charge-density-wave correlations has so far eluded a definitive answer. In particular, previous numerical simulations of Hubbard ladders have seen a much faster decay of superconducting correlations than expected based on analytical arguments. We revisit this question using a state-of-the-art implementation of the density matrix renormalization group algorithm that allows us to simulate larger system sizes with higher accuracy than before. Performing careful extrapolations of the results, we obtain improved estimates for the Luttinger liquid parameter and the correlation functions at long distances. Our results confirm that, as suggested by analytical considerations, superconducting correlations become dominant in the limit of very small doping.
The dualism between superconductivity and charge/spin modulations (the so-called stripes) dominates the phase diagram of many strongly-correlated systems. A prominent example is given by the Hubbard model, where these phases compete and possibly coexist in a wide regime of electron dopings for both weak and strong couplings. Here, we investigate this antagonism within a variational approach that is based upon Jastrow-Slater wave functions, including backflow correlations, which can be treated within a quantum Monte Carlo procedure. We focus on clusters having a ladder geometry with $M$ legs (with $M$ ranging from $2$ to $10$) and a relatively large number of rungs, thus allowing us a detailed analysis in terms of the stripe length. We find that stripe order with periodicity $lambda=8$ in the charge and $2lambda=16$ in the spin can be stabilized at doping $delta=1/8$. Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with $lambda=6$, appears at $delta=1/6$. Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at $delta=1/12$ and metallic with strong superconducting correlations at $delta=1/10$, as well as for intermediate (incommensurate) dopings. Remarkably, we observe that spin modulation plays a major role in stripe formation, since it is crucial to obtain a stable striped state upon optimization. The relevance of our calculations for previous density-matrix renormalization group results and for the two-dimensional case is also discussed.
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