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arXiv:1905.02658 · SciPost Physics

Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model

Luca F. Tocchio, Arianna Montorsi, Federico Becca

Published Aug 12, 2019• 31 citations
arXivHTMLPDF

Abstract

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 M legs (with M M ranging from 2 2 to 10 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 λ = 8 in the charge and 2\lambda=16 2 λ = 16 in the spin can be stabilized at doping \delta=1/8 δ = 1 / 8 . Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with \lambda=6 λ = 6 , appears at \delta=1/6 δ = 1 / 6 . Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at \delta=1/12 δ = 1 / 12 and metallic with strong superconducting correlations at \delta=1/10 δ = 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.

DOI
10.21468/scipostphys.7.2.021

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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 M legs (with M M ranging from 2 2 to 10 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 λ = 8 in the charge and 2\lambda=16 2 λ = 16 in the spin can be stabilized at doping \delta=1/8 δ = 1 / 8 . Here, there are no sizable superconducting correlations and the ground state has an insulating character. A similar situation, with \lambda=6 λ = 6 , appears at \delta=1/6 δ = 1 / 6 . Instead, for smaller values of dopings, stripes can be still stabilized, but they are weakly metallic at \delta=1/12 δ = 1 / 12 and metallic with strong superconducting correlations at \delta=1/10 δ = 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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') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.
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