DMRG study of the spin gap in a one dimensional Hubbard model: effect of the distant transfer and exchange coupling

TL;DR

This study uses DMRG to analyze how next-nearest neighbor hopping and ferromagnetic exchange influence the spin gap in a one-dimensional Hubbard model, revealing conditions that open or suppress the gap.

Contribution

It provides a detailed numerical investigation of the effects of distant transfer and exchange coupling on the spin gap in 1D Hubbard models, extending understanding beyond simple nearest-neighbor interactions.

Findings

Significant spin gap opens at half-filling when |t'| ≈ |t| and J=0.

The spin gap is suppressed by the introduction of ferromagnetic exchange J.

Quarter-filled systems exhibit very small spin gaps regardless of t' and J.

Abstract

The spin gap of a one-dimensional repulsive Hubbard model is numerically calculated with the density matrix renormalization group, with a special emphasis on the effect of a next-nearest neighbor hopping (t') and the nearest-neighbor ferromagnetic exchange (J) interaction. At half-filling, a significant spin gap opens if |t'| \simeq |t| and J=0, in agreement with the weak coupling theory, while the gap is strongly suppressed by the introduction of J. On the other hand, the quarter-filled system has very small spin gaps regardless of the values of t' and J. Implications for the CuO_2 chain in Sr_{14}Cu_{24}O_{41} and related materials are discussed.