SciPost Phys. 12, 180 (2022) ·
published 1 June 2022

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By using variational quantum Monte Carlo techniques, we investigate the instauration of stripes (i.e., charge and spin inhomogeneities) in the Hubbard model on the square lattice at hole doping $\delta=1/8$, with both nearest ($t$) and nextnearestneighbor hopping ($t^\prime$). Stripes with different wavelengths $\lambda$ (denoting the periodicity of the charge inhomogeneity) and character (bond or sitecentered) are stabilized for sufficiently large values of the electronelectron interaction $U/t$. The general trend is that $\lambda$ increases going from negative to positive values of $t^\prime/t$ and decreases by increasing $U/t$. In particular, the $\lambda=8$ stripe obtained for $t^\prime=0$ and $U/t=8$ [L.F. Tocchio, A. Montorsi, and F. Becca, SciPost Phys. 7, 21 (2019)] shrinks to $\lambda=6$ for $U/t\gtrsim 10$. For $t^\prime/t<0$, the stripe with $\lambda=5$ is found to be remarkably stable, while for $t^\prime/t>0$, stripes with wavelength $\lambda=12$ and $\lambda=16$ are also obtained. In all these cases, pairpair correlations are highly suppressed with respect to the uniform state (obtained for large values of $t^\prime/t$), suggesting that striped states are not superconducting at $\delta=1/8$.
SciPost Phys. 7, 021 (2019) ·
published 12 August 2019

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The dualism between superconductivity and charge/spin modulations (the socalled stripes) dominates the phase diagram of many stronglycorrelated 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 JastrowSlater 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 $2\lambda=16$ 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 densitymatrix renormalization group results and for the twodimensional case is also discussed.
SciPost Phys. 6, 018 (2019) ·
published 5 February 2019

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Shortrange antiferromagnetic correlations are known to open a spin gap in the repulsive Hubbard model on ladders with $M$ legs, when $M$ is even. We show that the spin gap originates from the formation of correlated pairs of electrons with opposite spin, captured by the hidden ordering of a spinparity operator. Since both spin gap and parity vanish in the twodimensional limit, we introduce the fractional generalization of spin parity and prove that it remains finite in the thermodynamic limit. Our results are based upon variational wave functions and Monte Carlo calculations: performing a finite sizescaling analysis with growing $M$, we show that the doping region where the parity is finite coincides with the range in which superconductivity is observed in two spatial dimensions. Our observations support the idea that superconductivity emerges out of spin gapped phases on ladders, driven by a spinpairing mechanism, in which the ordering is conveniently captured by the finiteness of the fractional spinparity operator.
Dr Tocchio: "The table of the energy differ..."
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