Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping

TL;DR

This paper explores the phase diagram of a one-dimensional Hubbard model with next-nearest-neighbor hopping, revealing a large ferromagnetic region, analyzing phase transitions, and comparing weak-coupling behavior to the two-chain Hubbard model.

Contribution

It provides a comprehensive analysis of the ferromagnetic phases and phase transitions in the extended Hubbard model, including numerical determination of critical exponents and Luttinger-liquid parameters.

Findings

A substantial ferromagnetic phase exists in the strong-coupling regime.

The transition from paramagnetic to ferromagnetic state is second order with numerically determined critical exponents.

Weak-coupling behavior can be mapped onto the two-chain Hubbard model, with explicit phase diagram and gap calculations.

Abstract

We study the phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping using exact diagonalization, the density-matrix renormalization group, the Edwards variational ansatz, and an adaptation of weak-coupling calculations on the two-chain Hubbard model. We find that a substantial region of the strong-coupling phase diagram is ferromagnetic, and that three physically different limiting cases are connected in one ferromagnetic phase. At a point in the phase diagram at which there are two Fermi points at weak coupling, we study carefully the phase transition from the paramagnetic state to the fully polarized one as a function of the on-site Coulomb repulsion. We present evidence that the transition is second order and determine the critical exponents numerically. In this parameter regime, the system can be described as a Luttinger liquid at weak coupling. We extract the Luttinger-liquid parameters and show how their behavior differs from that of the nearest-neighbor Hubbard model. The general weak-coupling phase diagram can be mapped onto that of the two-chain Hubbard model. We exhibit explicitly the adapted phase diagram and determine its validity by numerically calculating spin and charge gaps using the density-matrix renormalization group.