Stripes in the extended $t-t^{\prime }$ Hubbard model: A Variational Monte Carlo analysis

Abstract

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 next-nearest-neighbor hopping ($t^{\prime }$). Stripes with different wavelengths $\lambda$ (denoting the periodicity of the charge inhomogeneity) and character (bond- or site-centered) are stabilized for sufficiently large values of the electron-electron 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. {\bf 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, pair-pair 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 $\delta =1/8$.

18 pages, 10 figures, submission to SciPost

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• The Fractal-Lattice Hubbard Model
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• Transport anisotropy and metal-insulator transition in striped Dirac fermion systems
• Variational Monte Carlo study of stripes as a function of doping in the $t-t^{\prime }$ Hubbard model
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods