Phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping

TL;DR

This paper maps out the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping, revealing diverse phases including metallic, superconducting, and ferromagnetic states across different coupling regimes.

Contribution

It provides the first comprehensive phase diagram of the 1D Hubbard model with next-nearest-neighbor hopping using DMRG and Hartree-Fock methods, highlighting new phase behaviors.

Findings

Spin gap vanishes in the strong-coupling regime.

Multiple phases such as superconducting and ferromagnetic states are identified.

Contrasts with weak-coupling predictions of a spin-gapped liquid.

Abstract

We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group (DMRG) method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.