Phase diagram of the $t-t^{\prime }-U$ chain at half filling

Abstract

We study the half filled Hubbard chain including next-nearest-neighbor hopping $t^{\prime }$. The model has three phases: one insulating phase with dominant spin-density-wave correlations at large distances (SDWI), another phase with dominant spin-dimer correlations or dimerized insulator (DI), and a third one in which long distance correlations indicate singlet superconductivity (SS). The boundaries of the SDWI are accurately determined numerically through a crossing of excited energy levels equivalent to the jump in the spin Berry phase. The DI-SS boundary is studied using several indicators like correlation exponent $K_{\rho }$, Drude weight $D_c$, localization parameter $z_L$ and charge gap ${\Delta }_c$.

arXiv comment6 pages including 7 figures

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• Band-Insulator-Metal-Mott-Insulator transition in the half--filled $t-t^{\prime }$ ionic-Hubbard chain
• Ultracold fermions in a one-dimensional bipartite optical lattice: metal-insulator transitions driven by shaking
• Breakdown of the Luttinger sum-rule at the Mott-Hubbard transition in the one-dimensional t1-t2 Hubbard model
• Interaction induced Fermi-surface renormalization in the $t_1-t_2$ Hubbard model close to the Mott-Hubbard transition
• Filling-dependence of the zigzag Hubbard ladder for a quasi-one-dimensional superconductor Pr_2Ba_4Cu_7O_{15-delta}
• Comparative study of the density matrix embedding theory for the Hubbard models
• Simulating the Fermi-Hubbard model with long-range hopping on a quantum computer
• Repulsion driven metallic phase in the ground state of the half-filled $t-t^{\prime }$ ionic Hubbard chain