Doping $S=1$ antiferromagnet in one-dimension

TL;DR

This study investigates how doping affects the static and dynamic spin correlations in a one-dimensional $S=1$ antiferromagnetic Heisenberg model, revealing phases like orbital-RVB, coherent magnon behavior, and a spiral-like state near ferromagnetic transition.

Contribution

It provides a detailed analysis of doping effects on spin excitations and uncovers a new spiral-like phase in doped $S=1$ antiferromagnetic chains.

Findings

Orbital-RVB state persists up to doping level x ≈ 0.3.

Spin spectrum remains gapped with coherent magnons up to wavevector 2k_F.

Emergence of a spiral-like state near ferromagnetic transition.

Abstract

Antiferromagnetic ground states, when doped, give rise to rich and complex phenomena, prompting detailed investigations in various spin systems. Here, we study the effect of doping on the one-dimensional $S = 1$ antiferromagnetic Heisenberg model (AFM). Specifically, we investigate how the presence of holes affects the static and dynamic (frequency-dependent) spin-spin correlations of the two-orbital Hubbard-Kanamori chain. The latter, at half-filling and in the strong-interaction limit, maps onto an $S = 1$ Heisenberg model. For moderate interactions, an orbital resonating-valence-bond (orbital-RVB) state emerges up to doping levels of $x \lesssim 0.3$. A detailed analysis of interaction strength $U$ and doping concentration $x$ reveals that this phase inherits the key features of spin excitations found in the half-filled case -- namely, a gapped spin spectrum and ``coherent'' magnon behavior up to a wavevector $q$ determined by the Fermi vector, $2k_\mathrm{F} = \pi(1 - x)$. Furthermore, our results uncover an additional broad, incoherent spectral weight for $q \gtrsim 2k_\mathrm{F}$ at high frequencies. Finally, we show that near the transition to a ferromagnetic phase, a previously unidentified spiral-like state emerges, characterized by spin excitations reminiscent of the $J_1$-$J_2$ Heisenberg model.