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

TL;DR

This study uses variational quantum Monte Carlo to analyze stripe formations in the extended Hubbard model at 1/8 doping, revealing how stripe periodicity depends on interaction strength and hopping parameters, and showing suppressed superconductivity in these states.

Contribution

It provides a detailed variational Monte Carlo analysis of stripe stability and characteristics in the extended Hubbard model with next-nearest-neighbor hopping.

Findings

Stripe periodicity varies with $t'$ and $U/t$ values.

Stripe states are not superconducting at $ ho=1/8$ doping.

Stable stripe wavelengths depend on the sign of $t'$.

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 $\delta=1/8$.