First and second order ferromagnetic transition at T=0 in a 1D itinerant system

TL;DR

This paper investigates quantum phase transitions in a modified 1D Hubbard model with next-nearest-neighbor hopping, revealing first and second order ferromagnetic transitions at zero temperature through numerical methods.

Contribution

It demonstrates the nature of ferromagnetic transitions in the t1-t2 Hubbard chain, identifying conditions for first and second order quantum phase transitions at T=0.

Findings

Transition type depends on the phase being destabilized (Luttinger liquid or spin liquid).

First order transition occurs at large U when destabilizing the fully polarized state.

Second order transition corresponds to a quantum critical point at T=0.

Abstract

We consider a modified version of the one-dimensional Hubbard model, the t1-t2 Hubbard chain, which includes an additional next-nearest-neighbor hopping. It has been shown that at weak coupling this model has a Luttinger liquid phase or a spin liquid phase depending upon the ratio of t2 to t1. Additionally if the on-site interaction U is large enough, the ground state is fully polarized. Using exact diagonalization and the density-matrix renormalization group, we show that the transition to the ferromagnetic phase is either of first or second order depending on whether the Luttinger liquid or spin liquid is being destabilized. Since we work at T=0, the second order transition is a quantum magnetic critical point.