The Effective Theory of Hole Doped Spin-1 Chain

TL;DR

This paper develops an effective theory for hole-doped spin-1 chains, analyzing quasiparticle excitations, band structure, and spin correlations, revealing a critical hopping parameter and distinct behaviors in different regimes.

Contribution

It introduces a novel effective theoretical framework for understanding hole doping effects in spin-1 chains, including quasiparticle bands and spin structure factors.

Findings

Identification of two quasiparticle bands in the large t limit.

Discovery of a critical hopping value t_c=0.21Δ_H affecting band mixing.

Analysis of spin structure factor contributions in different t regimes.

Abstract

An effective theory for the hole doped spin-1 antiferromagnetic chain is proposed in this paper. The two branches of low energy quasipaticle excitation is obtained by the diagrammic technique. In the large t limit(in which t is the hole hopping term), the lower band is essentially the bound state of one hole and one magnon and the other band is the sigle hole state. We find a critical value of t, $t_c=0.21\Delta_H$(in which $\Delta_H$ is the Haldane gap).For $t>t_c$, with the decrement of t, the mixing of these two bands become stronger and stronger, and at the same time the effective band mass becomes larger and larger. When $t<t_c$ the minimum of the lower band moves away from zero the another point between zero and $\pi/2$. The spin strcture factor is also calculated in this paper, and we find that for large t limit the main contribution is from the inter-band transition which induce a resonant peak in the Haldane gap. While for small t limit the main contribution is from the intra-band transition which only cause a diffusion like broad bump in the Haldan gap.