One-dimensional metallic behavior of the stripe phase in La$_{2-x}$Sr$_x$CuO$_4$

Using an exact diagonalization method within the dynamical mean-field theory we study stripe phases in the two-dimensional Hubbard model. We find a crossover at doping $\delta\simeq 0.05$ from diagonal stripes to vertical site-centered stripes with populated domain walls, stable in a broad range of doping, $0.05<\delta<0.17$. The calculated chemical potential shift $\propto -\delta^2$ and the doping dependence of the magnetic incommensurability are in quantitative agreement with the experimental results for doped La$_{2-x}$Sr$_x$CuO$_4$. The electronic structure shows one-dimensional metallic behavior along the domain walls, and explains the suppression of spectral weight along the Brillouin zone diagonal.