发表机构
Technical University Dresden; Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿工业大学; 德累斯顿IFW理论固体物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过密度矩阵重整化群研究铁磁Hund耦合双t-J链中自旋-1 Haldane相在巡游掺杂下的稳定性，发现宽掺杂范围内保持拓扑特征并形成金属性C1S0相，最终过渡到高掺杂重入铁磁相。
AI 中文摘要
我们研究了由铁磁（FM）Hund交换耦合的两条t-J链中自旋-1 Haldane对称性保护拓扑（SPT）相的巡游空穴掺杂。密度矩阵重整化群计算表明，弦序、有限自旋隙和Haldane纠缠结构在广泛的掺杂范围内共存。结合与单一无能隙电荷模式一致的纠缠熵标度，这些结果支持具有C1S0低能描述的金属性掺杂Haldane SPT。在低掺杂下，短程电荷关联降低了自旋-1/2缺陷梯级的密度，而在较高掺杂下，它们的位置变得几乎不相关，同时它们的自旋被集体纳入关联自旋扇区。掺杂的Haldane SPT终止于完全自旋极化的FM相，该相在全局相图的高掺杂区域形成重入口袋。稀极限分析将两个FM边界追溯到弱Hund耦合下的自旋-电荷分解和强Hund耦合下伴随对迁移率降低的梯级三重态束缚。我们的结果表明移动载流子如何重组Haldane自旋结构，同时保留其特征签名。
英文摘要
We study itinerant hole doping of the spin-$1$ Haldane symmetry-protected topological (SPT) phase in two $t$--$J$ chains coupled by ferromagnetic (FM) Hund exchange. Density-matrix renormalization group calculations show that string order, a finite spin gap, and the Haldane entanglement structure coexist over a broad doping range. Combined with entanglement-entropy scaling consistent with a single gapless charge mode, these results support a metallic doped Haldane SPT with a $C1S0$ low-energy description. At low doping, short-range charge correlations reduce the density of spin-$1/2$ defect rungs, whereas at larger doping their positions become nearly uncorrelated while their spins are collectively incorporated into the correlated spin sector. The doped Haldane SPT terminates in a fully spin-polarized FM phase, which forms a reentrant pocket at high doping in the global phase diagram. Dilute-limit analyses trace the two FM boundaries to spin--charge factorization at weak Hund coupling and to rung-triplet binding with reduced pair mobility at strong Hund coupling. Our results show how mobile carriers reorganize the Haldane spin structure while preserving its characteristic signatures.
Comments6 pages, 4 figures, Supplemental Material
