AI 中文总结
研究半填充一维自旋费米子链中有限局部排斥对HK物理的影响，通过精确对角化计算相关量，发现哈伯德项能辅助强HK响应，而NN密度相互作用与之有竞争，为HK物理定点稳定性提供非微扰实空间补充。
AI 中文摘要
最近，初贝-小本（HK）模型被确定为莫特性的定点描述，对局部相互作用微扰具有稳定性。这引发了弱微扰范围之外的一个自然问题：有限的局部排斥如何在实空间可观测量和局域谱中改变HK物理？我们在半填充的一维自旋费米子链中解决这个问题，其中HK相互作用由在位哈伯德排斥补充。通过开放链中的精确对角化，我们计算基态关联函数和位点分辨的局域谱。我们发现哈伯德项不会使系统远离HK主导区域。相反，在适度的\(U_{\rm HK}\)下，有限的\(U_{\rm Hub}\)促进了在更大\(U_{\rm HK}\)时纯HK链特征行为的出现。这种哈伯德辅助的强HK响应一致地体现在正自旋关联的发展、单粒子相干性的抑制、杂质诱导的局域谱权重重新分布以及配对关联的演变中。作为对照微扰，我们将在位哈伯德相互作用替换为最近邻（NN）密度相互作用。与哈伯德情况相反，HK和NN相互作用表现出竞争趋势，并且不会再现相同的强HK行为。这些结果为HK物理的定点稳定性提供了非微扰实空间补充，并表明额外排斥相互作用的效果敏感地取决于其空间结构。
英文摘要
The Hatsugai-Kohmoto (HK) model has recently been identified as a fixed-point description of Mottness that is stable against perturbing local interactions. This raises a natural question beyond the weak-perturbation regime: how does a finite local repulsion modify HK physics in real-space observables and local spectra? We address this question in a half-filled one-dimensional spinful fermion chain, where the HK interaction is supplemented by an onsite Hubbard repulsion. Using exact diagonalization in an open chain, we compute ground-state correlation functions and site-resolved local spectra. We find that the Hubbard term does not drive the system away from the HK-dominated regime. Instead, at moderate $U_{\rm HK}$, a finite $U_{\rm Hub}$ promotes the emergence of behavior characteristic of the pure HK chain at larger $U_{\rm HK}$. This Hubbard-assisted strong-HK response is reflected consistently in the development of positive spin correlations, the suppression of single-particle coherence, the impurity-induced redistribution of local spectral weight, and the evolution of pairing correlations. As a control perturbation, we replace the onsite Hubbard interaction by a nearest-neighbor (NN) density interaction. In contrast to the Hubbard case, the HK and NN interactions display competing tendencies and do not reproduce the same strong-HK behavior. These results provide a nonperturbative real-space complement to the fixed-point stability of HK physics and show that the effect of an additional repulsive interaction depends sensitively on its spatial structure.
Comments14 pages,20 figures
